Profile book 2015

Transcription

Profile book 2015

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2015
Mathematics
@ IISER Pune
People in Math@IISER Pune
A Raghuram
Advait Phanse
Akash Krishna
Aman Jhinga
Amit Hogadi
Anindya Goswami
Anisa Chorwadwala
Anup Biswas
Anupam Singh
Ayan Mahalanobis
Ayesha Fatima
Baskar Balasubramanyam
Bhagyalaxmi
Bhakti Bhushan Manna
Chaitanya Ambi
Chandrasheel Bhagwat
Chitrabhanu Chaudhuri
Debangana Mukherjee
Debargha Banerjee
Diganta Borah
Dipramit Majumdar
Girish Kulkarni
Gunja Sachdeva
Hitesh Raundal
Jatin Majithia
Jyotirmoy Ganguly
K Hariram
Kalpesh Pednekar
Kaneenika Sinha
Krishna Kaipa
Makarand Sarnobat
Manidipa Pal
Milan Kumar Das
Mousumi Bhakta
Neha prabhu
Nishad Mandlik
Prabhat Kushwaha
Pralhad Shinde
Pranay Goel
Preeti
Rabeya Basu
Rama Mishra
Rashmi Kulkarni
Reshma Chandrasekharan
Rohit Joshi
Ronnie Sebastian
Sanket Nandan
Shirish Kulhari
Shiva Chidambaram
Soumen Maity
Steven Spallone
Sudhir Pujahari
Supriya Pisolkar
Sushil Bhunia
Suvarna Gharat
Tathagata Mandal
Tejas Kalelkar
Uday Jagadale
Uttara Naik-Nimbalkar
Vivek Mallick
Yasmeen Akhtar
Compiling, Editing and Design: Anisa Chorwadwala and Shanti Kalipatnapu
Photo Courtesy: Makarand Sarnobat, VS Rao, Anisa Chorwadwala, Stefan Friedl, and other contributors from IISER Pune
Cover Page: Pi value up to 10,000 digits taken from http://www.math.utah.edu/~pa/math/pi.html
Welcome Message
I am now into my fourth year
as
Coordinator
for
Mathematics at IISER Pune,
and life here, as always, is
full of new beginnings.
Starting this semester, all the
mathematics personnel are
now comfortably ensconced
in the top floor of the Main
Building at IISER Pune.
Such beginnings invariably
give a new energy and there
is this feeling that in front of
us is evolving a path that we
were born to take… a path
full of beautiful theorems and
pretty lemmas just waiting to
be proved by the eager
minds of IISER Pune!
The last year has seen us consolidate our strengths. We are now 22 regular faculty members, 1
INSPIRE fellow, and 1 visiting professor, 2 post-docs with possibly two more joining us later this
year. Our PhD program is now going very well, and it is a pleasure to see some of our students
blossoming into mathematicians. From this coming fall semester we will be starting an
integrated-PhD program. Our BS-MS students who graduated in 2014 got selected into topquality programs around the world such as University of Michigan, USA; University of
Washington at Seattle, USA; Essen University, Germany; INSEAD, France etc.
We have continued with our tradition of hosting high-profile events at IISER Pune. In June 2014,
there was an international workshop on “p-adic Aspects of Modular Forms” followed by the “29th
Annual Conference of the Ramanujan Mathematical Society.” The “Young Women and
Mathematics” symposium in July capped off a very busy summer. And, later in December, we
had “Advances in Mathematical Biology.” Events such as these go a long way in establishing
IISER Pune as a vibrant center for Mathematics!
A Raghuram
Professor and Coordinator
Mathematics, IISER Pune
Academic &
Administrative Support
Algebraic Geometry
One can describe algebraic geometry as the study of varieties, which are spaces
defined by vanishing of polynomial equations. I have been interested in moduli
spaces which are special types of varieties which parametrize geometric objects.
In the last couple of decades, people have succeeded in applying ideas from
topology, especially homotopy theory, to the study of algebraic varieties. This
interplay between homotopy theory and algebraic geometry has been one of my
latest fascinations.
Amit Hogadi
Associate Professor
Currently, I am working on problems which are sometimes clubbed under the title
homotopical algebraic geometry and have applications to K-theory, motivic
cohomology and also classical topics like Brauer groups.
[email protected]
Amit Hogadi received PhD from
Princeton University, USA in 2007.
He was at Tata Institute of
Fundamental Research (TIFR),
Mumbai, India before joining IISER
Pune in December 2013.
Selected Publications
With Indranil Biswas. Fundamental group of quotient singularities. To appear in International
Mathematics Research Notices.
Esnault, H. and Hogadi, A. (2012). On the algebraic fundamental group of smooth varieties in
characteristic p>0. Transactions of the American Mathematical Society 364:2429-2442.
Hogadi, A. and Mehta, V. (2011). Birational invariance of the S-fundamental group scheme. Pure and
Applied Mathematical Quarterly 7(4):1361-1370.
Hogadi, A. and Pisolkar, P. (2011). On the cohomology of Witt vectors of p-adic integers and a
conjecture of Hesselholt. Journal of Number Theory 131(10):1797-1807.
Hogadi, A. and Xu, C. (2009). Degenerations of rationally connected varieties. Transactions of the
American Mathematical Society 361(7):3931-3394.
Stochastic Control – Game
Theory, Math Finance, Queuing
Networks, Renewal Processes
I am exploring various topics in Applied Probability. Those include generalization
of Black-Sholes-Merton PDE for options in semi-Markov modulated market,
Föllmer Schweizer decomposition of an unattainable contingent claim, equilibrium
of non-cooperative semi-Markov game under ergodic cost, optimal control under
risk sensitive cost, portfolio optimization, large deviation limit, fluid limit in queuing
network, PDE techniques in stochastic control and differential games etc.
Anindya
Goswami
Assistant Professor
[email protected]
Anindya Goswami received his PhD
from Indian Institute of Science
(IISc), Bangalore, India in 2008.
Following this, he held postdoctoral
positions at the Universiteit Twente
in Enschede, The Netherlands;
INRIA in Rennes, France; and
Technion in Haifa, Israel before
joining IISER Pune in 2011.
I use Markov models, filtering techniques, stochastic calculus, infinitesimal
generator for semigroup of operators, mild solution technique for parabolic
equations, viscosity solution method for HJB/HJI equations, stability analysis of
numerical schemes for solving PDE or IE, convergence of value iteration
schemes, marginalization technique in rare event simulation for hybrid processes,
martingale formulation for Markov processes etc.
Goswami, A. and Saini, R.K. (2014). Volterra equation for pricing and hedging in a regime switching
market. Cogent Economics & Finance 1(2):1-11.
Atar, R., Goswami, A. and Shwartz, A. (2014). On the risk-sensitive cost for a Markovian multiclass
queue with priority. Electronic Communications in Probability 19(11):1-13.
Atar, R., Goswami, A. and Shwartz, A. (2013). Risk-sensitive control for the parallel server model.
SIAM Journal on Control and Optimization 51:4363-4386.
Basak, G.K., Ghosh, M.K. and Goswami, A. (2011). Risk minimizing option pricing for a class of exotic
options in a Markov modulated market. Stochastic Analysis and Applications 29:259-281.
Ghosh, M.K., Goswami, A. and Kumar, S.K. (2010). Portfolio optimization in a Markov modulated
market: Chapter in Modern Trends In Controlled Stochastic Processes: Theory and Applications.
Luniver Press, pp. 181-195.
Ghosh, M.K., Goswami, A. and Kumar, S.K. (2009). Portfolio optimization in a semi-Markov
modulated market. Applied Mathematics & Optimization 60:275-296.
Ghosh, M.K. and Goswami, A. (2009). Risk minimizing option pricing in a semi-Markov modulated
market. SIAM Journal on Control and Optimization 48:1519-1541.
Ghosh, M.K. and Goswami, A. (2008). Partially observable semi-Markov games with average payoff.
Journal of Mathematical Analysis and Applications 345:26-39.
Shape Optimization Problems
My research work falls mainly in the following two branches of Mathematics:
Partial differential equations and Riemannian geometry. I work on shape
optimization problems including isoperimetric problems. A typical shape
optimization problem is to find a shape which is optimal in the sense that it
minimizes a certain cost functional while satisfying given constraints. In many
cases, the functional being minimized depends on the solution of a given partial
differential equation defined on the variable domain.
Anisa M H
Chorwadwala
Assistant Professor
[email protected]
We have solved some shape optimization problems for a class of doubly
connected domains over Rank-one symmetric spaces of non-compact type.
Among the Rank-one symmetric spaces of compact type, we dealt only with the
n
n+1
with the induced metric. In fact, we gave a
case of S , the unit sphere in ℝ
uniform proof for all the three space forms. Here, the functionals to be optimized
were the energy functional and the principal frequency associated with the
Dirichlet boundary value problem and the Dirichlet Eigenvalue problem
respectively, for both linear as well non-linear operators, namely the Laplacian
and the p-Laplacian.
Anisa Chorwadwala received her
PhD from University of Mumbai in
2007. Following this, she held
postdoctoral positions at the
Institute of Mathematical Sciences
(IMSc), Chennai; Abdus Salam
International Centre for Theoretical
Physics (ICTP), Trieste, Italy; and
Tata Institute of Fundamental
Research (TIFR), Mumbai. She has
been on the faculty of IISER Pune
since April 2011.
Moving Plane Method for a punctured ball
on the unit sphere
Anisa, M.H.C. and Mahadevan, R. A shape optimization problem for the p-Laplacian. Proceedings of
the Royal Society of Edinburgh (Accepted for Publication).
Anisa, M.H.C., Mahadevan, R. and Toledo, F. (2015). On the Faber-Krahn inequality for the Dirichlet
p-Laplacian.
ESAIM:
Control,
Optimisation
and
Calculus
of
Variations
DOI:
10.1051/cocv/2014017
Anisa, M.H.C. and Vemuri, M.K. (2013). Two functionals connected to the Laplacian in a class of
doubly connected domains on rank one symmetric spaces of non-compact type. Geometriae
Dedicata 167(1):11-21.
Stochastic Controls and
Queuing Theory
My broad research area falls under Applied Probability. I am mainly interested in
stochastic controls, small noise diffusion, asymptotics of queuing networks and
many other related models.
Anup Biswas
Assistant Professor
[email protected]
Anup Biswas received his PhD from
TIFR-Centre for Applicable
Mathematics, Bangalore, India in
2011. He held postdoctoral
positions at Technion, Israel, and
University of Texas, Austin, USA
before joining IISER Pune.
In the last couple of years, I have worked on problems from queuing theory that
involves measure-valued process. Such processes have proven powerful in
modeling queuing networks with general service and reneging distributions.
Another important area of queuing theory is scheduling control where one looks
for a policy that optimizes certain cost associated to the model. I also work on
such control problems.
Arapostathis, A., Biswas, A. and Pang, G. Ergodic control of multi-class M/M/N+M queues in the
Halfin-Whitt regime. To appear in Annals of Applied Probability.
Atar, R., Biswas, A. and Kaspi, H. Fluid limits of G/G/ 1+G queues under non-preemptive EarliestDeadline-First discipline. To appear in Mathematics of Operation Research.
Biswas, A. (2014). Risk-sensitive control for the multiclass many-server queues in the moderate
deviation regime. Mathematics of Operation Research 39(3):908-929.
Atar, R. and Biswas, A. (2014). Control of the multiclass G/G/1 queue in the moderate deviation
regime. Annals of Applied Probability 24(5).
Conjugacy Questions and
Representation Theory of Groups
Conjugacy questions in group theory have been of interest for its connection with
the representation theory and they have not been understood very well for
Algebraic Groups over arbitrary field. Usually groups are difficult objects and one
studies them via their representations to get better understanding.
Anupam Kumar
Singh
Assistant Professor
[email protected]
After doing MSc (Mathematics)
from Indian Institute of Technology
(IIT) Kanpur, Anupam Singh worked
for his doctorate at Harish Chandra
Research Institute, Allahabad and
Indian Statistical Institute (ISI),
Bangalore, India and got PhD from
ISI in 2007. He held postdoctoral
positions at Tata Institute of
Fundamental Research (TIFR),
Mumbai and Institute of
Mathematical Sciences (IMSc),
Chennai, India before joining the
faculty of IISER Pune in 2008.
Let G (e.g. GLn) be an algebraic group defined over a field k. We denote the k
points of G by G(k) (e.g. GLn(k), SLn(k) etc.). An element t of G(k) is said to be
real if it is conjugate to its own inverse in G(k). I have been concerned with
finding real elements in algebraic groups. Very interestingly often it relates to
finding strongly real elements (the elements which are product of two involutions
in G(k)).
Apart from studying structure of real elements in Algebraic Groups over k, I also
looked at many examples such as linear groups, orthogonal groups, symplectic
groups and the groups of type G2 to get better understanding of the problem.
Finding real elements helps in the understanding of real characters of the group
which in turn give information about those complex representations of the group
which are either orthogonal or symplectic.
Gates, Z., Singh, A. and Ryan Vinroot, C. Strongly real classes in finite Unitary groups of odd
characteristic. To appear in the Journal of Group Theory.
Kulshrestha, A. and Singh, A. (2011). Real elements and Schur indices of a group. The Mathematics
Student 80:73-84.
Gill, N. and Singh, A. (2011). Real and strongly real classes in PGLn(q) and quasi-simple covers of
PSLn(q). Journal of Group Theory 14:461-489.
Gill, N. and Singh, A. (2011). Real and strongly real classes in SLn(q). Journal of Group Theory
14:437-459.
Public Key Cryptography
I work at the intersection of pure mathematics (group theory) and public key
cryptography. Cryptography, especially public key cryptography, is the backbone
of a modern society. It serves us with the required tools for online transactions
and trading, i.e., online commerce.
Ayan
Mahalanobis
Assistant Professor
[email protected]
Ayan Mahalanobis obtained his
PhD from Florida Atlantic
University, Boca Raton, USA in
2005. He was a Visiting Assistant
Professor at the Stevens Institute of
Technology, New Jersey, USA for a
few years before joining IISER
Pune in 2009.
My research aims to find new cryptograhic primitives and to build secure
protocols from that. We look for groups in which the discrete logarithm problem is
secure. My recent work has shown that the group of non-singular circulant
matrices over a finite field has some properties that make them attractive over the
discrete logarithm problem on a finite field. This new finding has opened a new
avenue in research of public key cryptography.
Mahalanobis, A. The ElGamal cryptosystem over circulant matrices (Submitted).
Mahalanobis, A. and Shah, J. (2014). A new guess-and-determine attack on the A5/1 stream cipher.
Computer and Information Science 7(1):115-124.
Mahalanobis, A. (2013). Are matrices useful in public-key cryptography? International Mathematical
Forum 8(39):1939-1953.
Mahalanobis, A. The MOR cryptosystem and extra-special p-groups. Proceedings of WCC 2012,
Castro Urdiales, Spain July 9-13, 2012 & To appear in Journal of Discrete Mathematics and
Cryptography.
Mahalanobis, A. (2013). The automorphism group of the group of unitriangular matrices over a field.
International Journal of Algebra 7(15):723-733.
Mahalanobis, A. (2012). A simple generalization of the ElGamal cryptosystem to non-abelian groups
II. Communications in Algebra 40:3583-3596.
Mahalanobis, A. (2010). The discrete logarithm problem in the group of non-singular circulant
matrices. Groups Complexity Cryptology 2:83-89.
Modular Forms and Galois
Representations
Baskar
Balasubramanyam
Assistant Professor
[email protected]
Baskar Balasubramanyam
completed his PhD from Brandeis
University, USA in 2007. In 200708, he was a postdoctoral fellow at
the Center for Advanced Study in
Mathematics at the Ben-Gurion
University of the Negev in Israel.
Following this, he was a Bateman
Instructor at California Institute of
Technology, USA during 2008-10.
He has been with IISER Pune since
September 2010.
My research interests are in Number Theory. A modular form is essentially a
function defined on the complex upper half-plane (everything above the real axis)
that behaves in a good way under transformations of certain 2x2 matrices with
integer entries. The expansion at infinity of such a function gives us a power
series whose coefficients have interesting arithmetic properties. An important
example of numbers that arise in such a way is the Ramanujan Tau function τ(n).
In order to understand these coefficients, it is useful to consider an object
attached to it called the L-function (these are generalizations of the Riemann zeta
function).
A Galois group is a set of permutations of roots of an irreducible polynomial. For
2
example, complex conjugation permutes the roots of x +1. It is possible to
represent such permutations by matrices. One of the problems in Number Theory
is to try and understand the Galois group by studying its representations. One
can also attach L-functions to Galois representations and in some cases modular
forms and Galois representations are related through their L-functions.
Balasubramanyam, B., Ghate, E. and Vatsal, V. (2013). On local Galois representations over totally
real fields. Manuscripta Mathematica 142:513-524.
Balasubramanyam, B. and Longo, M. (2010). ∧-adic modular symbols over totally real fields.
Commenterii Mathematici Helvetici 86:841-865.
Balasubramanyam, B. and Raghuram, A. Special values of adjoint L-functions and congruences for
automorphic forms on GL(n) over a number field (Submitted)
Representation Theory, Analysis &
Geometry of Locally Symmetric
Spaces, Number Theory
Chandrasheel
Bhagwat
Assistant Professor
[email protected]
Chandrasheel Bhagwat obtained
Bachelor of Science in Mathematics
from Fergusson College, Pune in
2003 followed by Master of
Mathematics at Indian Statistical
Institute, Bangalore in 2005. He
completed PhD in Mathematics
from Tata Institute of Fundamental
Research (TIFR) Mumbai, India in
2011 and spent a few months as a
postdoctoral fellow at IISER Pune.
He has received the DST-INSPIRE
faculty award and research grant in
2011 and has joined IISER Pune as
INSPIRE Faculty Fellow in March
2012. From December 1, 2014, he
has been working as an Assistant
Professor at IISER Pune.
The interplay between arithmetic, spectral theory and geometry was studied by
mathematicians like Selberg, Maass, and Sunada among many others. From the
last few years, I have been working on the study of arithmetic aspects of the
spectral theory and geometry of symmetric spaces. My thesis work involved
proving various analogues of the classical number theoretic results in the context
of symmetric spaces. I am also interested in the study of analytic properties of the
Zeta functions associated to a rank one locally symmetric space, which encode a
lot of spectral and geometric data. They can be considered as the spectral
counterparts of the Dedekind zeta functions associated to number fields. I would
like to look at some of the ìnverse problems’ on locally symmetric spaces with
the aid of the Zeta functions mentioned above.
In a joint work with Prof CS Rajan and Dr Supriya Pisolkar, we have established
some results which relate the notions of weak commensurability (introduced by
Prasad and Rapinchuk) and representation equivalence of arithmetic lattices in
Lie groups. These notions are in turn related to the geometry and spectral theory
of the locally symmetric spaces defined by them. I am currently working (jointly
with Dr Supriya Pisolkar) on some of the related problems on discrete subgroups
of Lie groups.
My joint work with Prof Raghuram establishes period relations for the tensor
product of motives which together with the celebrated Deligne’s conjecture;
predict the results of a similar nature about the special values of Rankin - Selberg
L-functions and Dirichlet L-series. I am interested in working on some related
problems about special values for automorphic L-functions associated to
representations of algebraic groups; using techniques like Cohomology of
sheaves and Langlands constant term theory.
Bhagwat, C. (2015). On Deligne's periods for tensor product motives. Comptes rendus –
Mathématique 353:191-195.
Bhagwat, C., and Raghuram, A. (2013). Ratios of periods for tensor product motives. Mathematical
Research Letters 20(4):615-628.
Bhagwat, C., Pisolkar, S., and Rajan, C.S. (2013). Commensurability and representation equivalent
arithmetic lattices. International Mathematics Research Notices (IMRN) doi:10.1093/imrn/rns282.
Bhagwat, C. and Rajan, C.S. (2011). On a multiplicity one property for the length spectra of even
dimensional
compact
hyperbolic
spaces.
Journal
of
Number
Theory
doi:10.1016/j.jnt.2011.05.009.
Bhagwat, C. and Rajan, C.S. (2010). On a spectral analogue of the strong multiplicity one theorem.
International Mathematics Research Notices doi:10.1093/imrn/rnq243.
Automorphic Forms and
Arithmetic Geometry
In arithmetic geometry, we study the integral solutions of polynomial equations. In
arithmetic geometry we usually work over non-algebraically closed fields (like
rational numbers), and often in fields of non-zero characteristic (like finite fields),
and we may even restrict ourselves even to rings that are not a field (like
integers). We use the rich theory of modular forms (more generally, automorphic
representations) to find these solutions.
Debargha
Banerjee
Assistant Professor
[email protected]
Debargha Banerjee received his
PhD degree from Tata Institute of
Fundamental Research, Mumbai.
He earned his Master’s degree in
Mathematics from Indian Statistical
Institute and BSc from St Xavier’s
College, Kolkata. He got the
Australian Research council
Discovery postdoctoral fellowship
for 2 years at the Australian
National University, Canberra,
Australia. He was a visiting scientist
at the IMSC, Chennai, India and
later a guest scientist at the Max
Planck institute of Mathematics,
Bonn, Germany before joining
IISER Pune in November 2013.
Modular forms/ automorphic forms are generalizations of the periodic functions
like sine or cosine. The theory of modular forms made major contributions in
several important discoveries in modern mathematics, including the uniform
boundedness of torsion point of elliptic curves.
I am interested in understanding objects in geometry called “motives” and objects
in
analysis
called
automorphic
representations.
The
overarching
bridge/conjecture of Langlands connects these two fairly faraway worlds. I am
interested in understanding the integral and $p$-adic bridges that connect these
two beautiful universes.
In the automorphic universe, I wish to focus on modular symbols and special
values of L-functions (one of the main objects of study in the Langlands'
program). Motives can be described by different cohomology theories. I wish to
understand and use different cohomology theories using modular symbols, which
in turn give insights into special values of L-functions.
In another work, I developed the theory of differential modular forms for Shimura
curves over totally real fields. The differential modular forms were invented by
Buium and his collaborators. These work open the p-adic bridge of certain
automorpic forms.
Banerjee, D. (2014). A note on the Eisenstein elements of prime square level. Proceedings of the
American Mathematical Society 142:3675-3686.
Banerjee, D. (2014). Differential modular forms on Shimura curves over totally real fields. Journal of
Number Theory 135:353-373.
Banerjee, D. and Ghate, E. (2013). Adjoint lifts and modular endomorphism algebras. Israel Journal of
Mathematics 195(2):507-543.
Banerjee, D. and Ghate, E. (2011). Crossed product algebras attached to weight one forms.
Mathematical Research Letters 18(1):139-149.
Banerjee, D., Ghate, E. and Kumar, N. (2010). ∧-adic forms and the Iwasawa main conjecture.
Iwasawa Theory of totally real Fields (Proceedings of a Workshop held at IIT Guwahati,
published by Ramanujan Mathematical Society) 2010, No. 12. pp.15-47.
Banerjee, D. and Krishnamoorthy, S. The Eisenstein elements inside the space of modular symbols
(Submitted).
Banerjee, D. and A. Raghuram, p-adic L-functions for GLn (preprint, expository article)
Several Complex Variables
My research interests are in Several Complex Variables, Potential Theory and in
Differential Geometry. In the past, I studied various properties of a Kahler metric,
n
known as the Robin metric defined on bounded pseudoconvex domains in C ,
n>1. This metric was constructed by N. Levenberg and H. Yamaguchi using the
Robin function that arises from the Green function associated to the standard
Laplacian in C^n.
Diganta Borah
Assistant Professor
[email protected]
Diganta Borah received his PhD
from the Indian Institute of Science
(IISc), Bangalore, India in 2010 and
was a Research Associate there
until 2011. He joined IISER Pune in
January 2012.
Currently, I am studying various questions related to the motion of critical points
and the differential geometry of level lines of the Green function of a bounded
multiply connected domain in the complex plane. I am also investigating
properties of the metric induced by the capacity function on such domains.
Remarks on the metric induced by the Robin function III (Submitted).
Borah, D. (2013). Remarks on the metric Induced by the Robin Function II. Michigan Mathematical
Journal 62(3):581-630.
Borah, D. and Verma, K. (2011). Remarks on the metric induced by the Robin function. Indiana
University Mathematics Journal 60:751-802.
Analytic Number Theory,
Harmonic Analysis and Arithmetic
Geometry
Kaneenika Sinha
Assistant Professor
[email protected]
Kaneenika Sinha completed her
PhD from Queen's University,
Canada in 2006. She has held
postdoctoral fellowships at
University of Toronto, University of
Alberta and Mathematical Sciences
Research Institute, Berkeley. She
was an assistant professor in IISER
Kolkata before joining IISER Pune
in December 2012.
My primary research work is concerned with extremal functions in Fourier
analysis, equidistribution of Fourier coefficients of modular cusp forms, EichlerSelberg trace formula and arithmetic of modular curves. Modular forms play an
extremely important role in number theory and their Fourier coefficients carry
fundamental information about points of elliptic curves over finite fields, values of
the partition function, class numbers and representations of integers by quadratic
forms. They are essential tools in addressing many fundamental problems in
Mathematics, like Fermat's Last Theorem. Modular forms are a special case of
automorphic representations and lead to the Langlands program, a theme that
drives much of the twenty first century research in number theory and
representation theory. My research program focuses on the behavior of the
Fourier coefficients of normalized Hecke eigenforms and their connections with
Jacobian varieties of modular curves.
My research program in number theory heavily draws ideas and techniques from
various mathematical areas, like harmonic analysis and arithmetic geometry. The
problems pursued by me are posed in the language of algebra and geometry,
where as the techniques used in resolving them come from harmonic analysis.
Moreover, a comprehensive understanding of these questions necessitates
approaching them from a representation-theoretic point of view.
Bucur, A., David, C., Feigon, B., Lalín, M. and Sinha, K. (2012). Distribution of zeta zeroes of ArtinSchreier covers. Mathematical Research Letters.
Lalín, M. and Sinha, K. (2011). Higher Mahler measure for cyclotomic polynomials and Lehmer's
question. The Ramanujan Journal 26:257-294.
Ram Murty, M. and Sinha, K. (2010). Factoring newparts of Jacobians of certain modular curves.
Proceedings of the American Mathematical Society 138:3481-3494.
Ram Murty, M. and Sinha, K. (2009). Effective equidistribution of eigenvalues of Hecke operators.
Journal of Number Theory 129:681-714.
Algebraic Geometric Coding
Theory
My recent work is about studying Error Correcting Codes from the viewpoint of
projective geometry over finite fields.
To give a flavour of the kind of questions I am working on currently, consider k by
n matrices over a finite field with q elements (say q is odd) such that all k by k
minors of this matrix are nonzero. Let us call such a matrix MDS.
Krishna Kaipa
Assistant Professor
[email protected]
Krishna Kaipa obtained a BTech
from IIT Bombay and an MS
degree from University of Maryland
College Park, both in Mechanical
Engineering. He then pursued a
PhD in Mathematics from University
of Maryland, College Park. He held
assistant professor positions at IIT
Bombay and IISER Bhopal before
moving to IISER Pune in 2014.
Question: What can we say about 3 by q+1 MDS matrices?
Segre showed that any such matrix is row equivalent to a matrix whose columns
lie on the conic y^2 = xz.
Question: Do there exist k by q+2 MDS matrices when k <q?
The negative answer to this question is the main conjecture about MDS
matrices/codes.
Kaipa, K. (2014). An asymptotic formula in q for the number of [n,k] q-ary MDS codes. IEEE
Transactions on Information Theory 60(11):7047-7057.
With Harish Pillai (2013). Weight spectrum of codes associated with the Grassmannian G(3,7), IEEE
Transactions on Information Theory 59(2):986-993.
With Sudhir Ghorpade (2013). Automorphism groups of Grassmann codes, Finite fields and its
Applications 23:80-102.
With Peter Grinevich (2009). Multiscale limit for finite-gap Sine-Gordon Solutions and Calculation of
Topological Charge using Theta-functional Formulae. Proceedings of Steklov Mathematical
Institute 266(1):49-58.
Elliptic Partial Differential
Equations
My research interest includes semilinear and quasilinear elliptic partial differential
equations arising from geometry and physics. I study existence/nonexistence of
positive/sign-changing solutions, qualitative properties of solutions, regularity
properties etc using the techniques from nonlinear analysis.
Mousomi Bhakta
Assistant Professor
[email protected]
Mousomi Bhakta received her PhD
from TIFR-Centre for Applicable
Mathematics, Bangalore, India in
August, 2011. After that she held
visiting scientist position in ICTP,
Trieste, Italy for two months. Next,
she had postdoctoral positions at
Technion, Israel for two years and
University of New England, NSW,
Australia for one year before joining
IISER Pune in August 2014.
One of my main research areas is studying the second order and fourth order
semilinear and quasilinear elliptic equations with singularity. Such second order
equations for example, Hardy-Sobolev type equations arise in astrophysics.
Fourth order equations, for example, equations with biharmonic operator arise in
continuum mechanics, bio-physics, geometry. In particular, in the modeling of thin
elastic plates, clamped plates and in the study of the Paneitz-Branson equation
etc.
The other area of my research is studying the semilinear elliptic equations with
measure data, generalized boundary trace and generalized boundary value
problems.
Bhakta, M. A note on semilinear elliptic equation with biharmonic operator and multiple critical
nonlinearities. To appear in Advanced Nonlinear Studies.
Bhakta, M. (2015). Entire solutions for a class of elliptic equations involving p-biharmonic operator
and Rellich potentials. Journal of Math Analysis and Applications 423(2).
Bhakta, M and Marcus, M. (2014). Semilinear elliptic equations admitting similarity transformations.
Journal of Functional Analysis 267(10).
Bhakta, M. and Marcus, M.(2014). Reduced limit for semilinear boundary value problems with
measure data. Journal of Differential Equations 256(8).
Bhakta, M, and Musina, R. (2012). Entire solutions for a class of variational problems involving the
biharmonic operators and Rellich potentials. Nonlinear Analysis 75(9).
Bhakta, M. and Sandeep, K. (2012). Poincar’e-Sobolev equations in the hyperbolic space. Calculus of
Variations and Partial Differential Equations 44(1-2).
Bhakta, M, and Biswas, A. (2011). Hardy-Sobolev type equations for p-Laplacian, 1<p<2, in bounded
domain. Differential and Integral Equations 24(1-2).
Bhakta, M. and Sandeep, K. (2009). Hardy-Sobolev-Mazy’a type equations in bounded domains,
Journal of Differential Equations 247(1).
Dynamical Systems Modeling of
Multiscale Phenomena in Biology
Dynamical processes in biology naturally span several systems and multiple
scales, both in space and in time. We are interested in studying the dynamical
behavior of biological processes through mathematical modeling to complement
experimental understanding. My research focuses primarily on theoretical
neuroscience, cardiac dynamics and diabetes. Each of these areas is rich with
issues that arise from a fundamental need to develop theoretical frameworks, and
to handle multiscale dynamics within those.
Pranay Goel
Assistant Professor
[email protected]
Pranay Goel received his PhD in
Physics at the University of
Pittsburgh, USA. His postdoctoral
work was carried out at the
Mathematical Biosciences Institute,
The Ohio State University, and at
the Laboratory of Biological
Modeling, NIDDK, National
Institutes of Health, USA. He joined
the Mathematics and Biology
faculty at IISER Pune in 2009.
Our understanding of glucose-stimulated insulin secretion from the pancreatic
endocrine tissue, the islets of Langerhans, has developed considerably over the
last three decades. Much of my recent work has been related to analyzing some
newly proposed models of islet voltage oscillations (called “bursting”) that
implicate both ionic as well as metabolic activity as being jointly responsible for
function. Simultaneously, we are also interested in modeling and analysis of data
collected from patients diagnosed with Type 2 diabetes. This is joint work with
researchers at the University of Pune and K. E. M. Hospital, Pune.
Although we are a dry lab, since such research is highly interdisciplinary in
nature, we collaborate extensively with experimentalists.
Goel, P. and Sherman, A. (2009). The geometry of bursting in the dual oscillator model of pancreatic
beta-cells. SIAM Journal on Applied Dynamical Systems (SIADS) 8:1664-1693.
Goel, P., Sherman, A. and Friedman, A. (2009). Multiscale modeling of electrical and intracellular
activity in the pancreas: The islet Tridomain equations. SIAM Multiscale Modeling and Simulation
7:1609-1642.
Zhang, M., Fendler, B. Peercy, B., Goel, P., Bertram, R., Sherman, A., Satin, L. (2008). Long lasting
synchronization of calcium oscillations by cholinergic stimulation in isolated pancreatic islets.
Biophysical Journal 95:4676-4688.
Higgins, E.R., Goel, P., Puglisi, J.L., Bers, D.M., Cannell, M. and Sneyd, J. (2007). Modeling calcium
microdomains using homogenization. Journal of Theoretical Biology 247:623-644.
Goel, P., Sneyd, J. and Friedman, A. (2006). Homogenization of the cell cytoplasm: The calcium
bidomain equations. SIAM Multiscale Modeling and Simulation 5:1045-1062.
Classical Algebraic K-theory
My work is based on problems in classical K-theory which are related to Serre’s
problem on projective modules, widedly known as Quillen-Suslin theorem.
One of such problem is Quillen-Suslin’s local-global principle. This was one of the
main ingredient for the proof of Serre’s problem. I work on the matrix version of
this theorem introduced by A. Suslin to give a simpler proof of the theorem. There
are many generalizations and variations of this local-global technique for different
types of classical groups. I have worked for general quadratic and general
Hermitian groups.
Rabeya Basu
Assistant Professor
[email protected]
Rabeya Basu received her PhD
Research (TIFR), Mumbai, India in
2007. She then undertook
postdoctoral work initially at Harish
Chandra Research Institute,
Allahabad and later as an NBHM
Fellow at the Indian Statistical
Institute, Kolkata, India. She was in
IISER Kolkata as an assistant
professor before joining IISER Pune
in 2010.
Another type of problems is stabilization of K1 functor and the structure of
unstable K1 Groups. These problems are also studied for different types of
classical groups. Recently, I have studied the solvability property of the unstable
K1 group for the general Hermitian group.
Our method of proof can be used uniformly for many other classical groups. In
my PhD thesis we have given the uniform treatment for general linear, symplectic
and orthogonal groups. We have also deduced a module theoretic version of
local-global principle which is useful to generalize results from the free case to
the module case. At present I am working on this local-global principle for the
transvection subgroup of the general quadratic module.
Basu, R. Local-global principle for the general quadratic and the general Hermitian groups and the
nilpotence of KH1 (Submitted).
Basu, R. (2013). On elementary subgroup of GLn over rings. Ramanujan Mathematical Society
Newsletter 24(3).
Basu, R. (2011). Absence of torsion for NK1(R) over associative rings. Journal of Algebra and its
Applications 10:793-799.
Basu, R. and Rao, R.A. (2010). Injective stability for K1of regular rings. Journal of Algebra 323:367377.
Bak, A., Basu, R. and Rao, R.A. (2010). Local-global principle for Transvection groups. Proceedings
of the American Mathematical Society 138:1191-1204.
Basu, R. and Sridharan, R. (2007). An expository article: On Forster's conjecture and related results.
Punjab University Research Journal.
Low Dimensional Topology
For a reasonably long period of time my research focused around the Polynomial
representation of long knots. It was motivated by the issue of settling a long
lasting conjecture of Abhayankar. We established the equivalence between
polynomial isotopic classes of long knots with the ambient isotopic classes of
classical knots. Thus the entire knot theory can be done over polynomial knot
category. I am trying to compute some numerical knot invariants such as
unknotting number through polynomial knot theory.
Rama Mishra
Associate Professor
[email protected]
Rama Mishra has obtained her PhD
from Indian Institute of Technology
(IIT) Bombay, India in 1994. She
spent a few years with Harish
Chandra Research Institute,
Allahabad and Indian Statistical
Institute, Delhi as a postdoctoral
fellow and then served as a faculty
at IIT Kharagpur and IIT Delhi for
several years. She worked as a
JSPS fellow at Osaka City
University, Japan for one year and
as a visiting faculty at Boise State
University, USA before joining
IISER Pune.
Quantum topology is one of the emerging research areas. Many knot invariants
naturally arise through nice matrix algebra representation of interesting quantum
groups. They have been related to several models in statistical mechanics. I
would like to explore some models that are related to Singular knot theory.
I am also interested in classical knot invariants and their application in
mathematics and biological sciences. My joint work with Prof Louis Kauffman on
nodal parity invariants of knotted rigid vertex graphs discusses the application of
this invariant on protein folding classification.
Mishra, R. (2014). Polynomial unknotting and singularity index. Kyungpook Mathematical Journal
54(2):271-292.
Kauffman, L. and Mishra, R. (2013). Nodal parity invariants for knotted rigid vertex graphs. Journal of
Knot Theory and its Ramifications 22(4):1340002.
Mishra, R. and Bhushan, S. (2012). Knot theory in understanding proteins. Journal of Mathematical
Biology 65:1187-1213.
Prabhakar, M. and Mishra, R. (2009). Minimal degree sequence for torus knots of type (p,q). Journal
of Knot Theory and its Ramifications 18:485-491.
Prabhakar, M. and Mishra, R. (2009). Polynomial representation for long knots. International Journal
of Mathematical Analysis 3:325-337.
Mishra, R. (2006). Polynomial representations of strongly invertible knots and strongly negative
amphicheiral knots. Osaka Journal of Mathematics 43:625-639.
Prabhakar, M. and Mishra, R. (2006). Minimal degree sequence of 2–bridge knots. Fundamenta
Mathematicae 3:190.
Number Theory, Representation
Theory and Automorphic Forms
My group is currently studying the arithmetic properties of special values of
automorphic L-functions.
A Raghuram
Professor and Coordinator
[email protected]
After getting a BTech in Computer
Science and Engineering from
Indian Institute of Technology (IIT)
Kanpur, Raghuram moved to
Mathematics and got a PhD in
Mathematics in 2001 from the Tata
Institute of Fundamental Research
(TIFR), Mumbai, India. He had
postdoctoral positions at University
of Toronto, Canada and TIFR,
Mumbai, India and visiting assistant
professorships at Purdue University
and University of Iowa, USA. He
joined Oklahoma State University,
USA in 2006 as a tenure-track
assistant professor and was
promoted to associate professor
with tenure in 2011.Raghuram
joined IISER Pune in December
2011 as a Professor and the
Coordinator of Mathematics. His
research has been partially funded
by the National Science
Foundation, USA, and the
Alexander von Humboldt
Foundation, Germany.
The earliest prototype of a special value of an L-function is the classical formula
by Euler which says that the sum ∑ 1/n^2 of reciprocals of squares of all positive
integers is π^2/6. More generally, suppose M = {a_n} is a sequence of numbers
coming from some interesting data, for example, a_p can be the number of
solutions of an equation modulo a prime p, then a guiding principle in modern
number theory says that to study the sequence M one should study the L-function
L(s, M) = ∑ a_n/n^s. One can glean much information about the sequence M by
studying first the analytic properties, and second the arithmetic properties of
L(s,M).
The Langlands program, considered by many as a grand unifying principle in
modern mathematics, bridges different areas of mathematics, like geometry
(elliptic curves), number theory (Galois representations) and representation
theory (automorphic forms). The central theme making these bridges possible is
the notion of an L-function.
Our work uses the results and techniques of the Langlands program to prove
theorems about special values of various L-functions. These values encode
within them a lot of arithmetic and geometric information of the objects to which
the L-functions are attached. In earlier work stemming from my thesis, we have
also studied the representation theory and harmonic analysis of p-adic groups.
Selected Publications and Editorial Work
Critical values for Rankin-Selberg L-functions for GL(n) x GL(n-1) and the symmetric cube L-functions
for GL(2). To appear in Forum Mathematicum.
The Bloch – Kato Conjecture for the Riemann Zeta Function, Editors: John Coates, A. Raghuram,
Anupam Saikia and R. Sujatha. pp. 312 To be published by Cambridge University Press.
With Harald Grobner. On the arithmetic of Shalika models and the critical values of L-functions for
GL(2n). With an appendix by Wee Teck Gan. American Journal of Mathematics 136 (2014) 675728.
With Chandrasheel Bhagwat. Ratios of periods of tensor product motives. Mathematical Research
Letters 20 (2013) No. 4, 615-628.
With Wee Teck Gan. Arithmeticity for periods of automorphic forms. To appear in the Proceedings of
the International Colloquium on “Automorphic representations and L-functions,” held in TIFR
Mumbai, January 2012.
With Günter Harder. Eisenstein cohomology and ratios of critical values of Rankin-Selberg Lfunctions. C. R. Acad. Sci. Paris, Ser. I 349 (2011) 719-724.
With Naomi Tanabe. Notes on the arithmetic of Hilbert modular forms. Journal of the Ramanujan
Mathematical Society 26(3) (2011) 261-319.
On the special values of certain Rankin-Selberg L-functions and applications to odd symmetric power
L-functions. International Mathematical Research Notices (2010) No. 2, 334-372.
Algebraic Geometry
Ronnie Sebastian
My research so far has dealt with questions in algebraic geometry. More
specifically, with problems related to cycles on abelian varieties and problems
related to moduli of vector bundles on curves and surfaces. In cycles I have been
interested in a conjecture of Voevodsky which says that smash equivalence is the
same as numerical equivalence. This conjecture has some very nice
consequences, for instance, it implies that numerical and homological
equivalence coincide, which is suggested by the standard conjectures of
Grothendieck. My work on moduli of vector bundles has focused on proving
Torelli theorems and theorems on rationality of vector bundles. I am currently
focusing on expanding my research to number theory.
INSPIRE Faculty Fellow
[email protected]
After a Masters’ in Mathematics and
Scientific Computing from Indian
Institute of Technology (IIT) Kanpur,
Ronnie Sebastian did a PhD with V
Srinivas and Indranil Biswas at Tata
Institute of Fundamental Research
(TIFR), Mumbai. He then pursued
postdoctoral research at the
Institute of Mathematical Sciences,
Chennai; Humboldt University,
Berlin as an IMU Berlin Einstein
Foundation Fellow; and at the
Indian Statistical Institute,
Bangalore before joining IISER
Pune in May 2013.
Sebastian, R. (2013). Smash nilpotent cycles on varieties dominated by products of curves.
Compositio Mathematica 149(9):1511-1518.
Biswas, I. and Sebastian, R. (2013). On rationality of moduli spaces of vector bundles on real
Hirzebruch surfaces. Proceedings of the Indian Academy of Sciences Mathematical Sciences
123(2):213-223.
Combinatorics − covering arrays,
and cryptography
I am mostly interested in combinatorial problems. More specifically, I have been
working on covering arrays on hypergraphs, and construction of cryptographically
important Boolean functions.
Soumen Maity
Associate Professor
[email protected]
Soumen Maity received a PhD from
the Theoretical Statistics &
Mathematics Unit at Indian
Statistical Institute, Kolkata, India in
2002. He has postdoctoral
experience from Lund University
Sweden; Indian Institute of
Management (IIM) Kolkata, India;
and University of
Ottawa, Canada. Prior to joining
IISER Pune in 2009, he was at
Indian Institute of Technology (IIT)
Guwahati and Indian Institute of
Technology (IIT) Kharagpur, India.
Covering Arrays on Hypergraphs: Covering arrays are combinatorial structures
which extend the notion of orthogonal arrays and have applications in the realm
of software and circuit testing. A covering array of strength three is an array with
the property that any three rows are qualitatively independent. A covering array is
optimal if it has the minimum number of columns among covering arrays with the
same number of rows. We work on upper and lower bounds on the size of
covering arrays on hypergraphs based on hypergraph homomorphism.
Cryptography: Boolean functions are used as nonlinear combining functions in
LFSR based stream ciphers. A Boolean function is said to be resilient if its output
leaks no information about its input values. My research in this area presents
some strategies to modify the bent functions, by toggling some of its outputs, in
getting a large class of 1-resilient functions with very good nonlinearity and
autocorrelation.
Akhtar, Y, Maity, S. and Chandrasekharan, R.C. Covering arrays of strength four and software
testing. To appear in Springer Proceedings in Mathematics and Statistics.
Maity, S., Arackaparambil, C. and Meyase, K. (2013). A new construction of resilient Boolean
functions with high nonlinearity. Ars Combinatoria 109:171-192.
Maity, S. (2012). 3-Way software testing with budget constraints. IEICE Trans. Information & Systems
E95-D (9): 2227-2231.
Akhtar, Y. and Maity, S. (2012). Mixed covering arrays on hypergraphs. Communications in Computer
and Information Science 305:327-338.
Representation Theory and
Canonical Forms
A basic theme in representation theory for a topological group is the duality
between the geometry of the group and its spectral theory. In one project, I study
arithmetically interesting representations called “discrete series” using this
duality. I attempt to write their multiplicities in terms of measures over conjugacy
classes of p-adic groups.
Steven Spallone
Associate Professor
[email protected]
Steven Spallone received his PhD
from the University of Chicago,
USA in 2004. Afterwards he did
postdoctoral work at the MaxPlanck Institute in Bonn, at Purdue
University, and at the University of
Oklahoma, USA. He also visited the
Tata Institute of Fundamental
Research (TIFR) Mumbai, India. He
joined the faculty of IISER Pune in
July 2012.
In another project, I study representations of isometry groups of quadratic forms,
notably those induced from a stabilizer P of a nondegenerate subspace. I show
that relationships between such representations are illuminated by first
decomposing P into two subgroups M and N, and then byfinding canonical forms
for the conjugation action of M on N.
To introduce another project, consider square matrices, with entries modulo a
cubefree integer. I study the question of when two such matrices are conjugate. I
have also written some papers regarding when two germs of dynamical systems
fixing a point are conjugate, in the p-adic setting.
Spallone, S. (2012). Stable trace formulas and discrete series representations. Pacific Math Journal
256:435-488.
Jenkins, A. and Spallone, S. (2012). Local analytic conjugacy of semi-hyperbolic mappings in two
variables, in the non-archimedean setting. International Journal of Mathematics 23:1250059.
Shahidi, F. and Spallone, S. (2010). Residues of intertwining operators for SO(6) as character
identities. Compositio Mathematica 146:772-794.
Spallone, S. (2008). Residues of intertwining operators for classical groups. International Mathematics
Research Notices 056:37.
Margalit, D. and Spallone, S. (2007). A homological recipe for pseudo-Anosovs. Mathematical
Research Letters 14:853-863.
Number Theory, Galois
Cohomology, Arithmetic Aspects
of Symmetric Spaces
Broadly speaking, my area of research is number theory and I have been working
on problems mostly related to local fields. My thesis deals with questions having
a common theme of understanding behavior of norm maps in Galois extensions
of local fields. As an application, I computed the Chow group of Zero-cycles of
degree zero on Châtelet surfaces over local fields. This work relies on the work of
Bloch, Swinnerton-Dyer, Colliot-Téllène, Sansuc.
Supriya Pisolkar
Assistant Professor
[email protected]
Supriya Pisolkar obtained her PhD
degree from Harish Chandra
Research Institute, Allahabad, India
in 2010. She was a postdoctoral
fellow at Tata Institute of
Fundamental Research, Mumbai for
about three years before joining
IISER Pune in December 2013.
In joint work with Dr A Hogadi, we proved a conjecture of Hesselholt which
1
predicts the vanishing of the cohomology group H (G(L/K),W(OL)) for a Galois
extension of local fields L/K. This can be seen as an analogue of Hilbert theorem90. In the future, I would like to work on generalizations of this result.
Over the last couple of years I have also been fascinated by arithmetic aspects of
locally symmetric spaces which are special type of manifolds. The theory of
locally symmetric spaces is a beautiful amalgamation of theory of Lie groups,
algebraic groups, analysis, differential geometry, representation theory. In a joint
work with Prof CS Rajan and Dr C Bhagwat we have studied questions related to
commensurability type problems of these spaces.
Currently, I am interested in understanding the work of Gopal Prasad and
Rapinchuk which establishes a connection between arithmetic and geometric
aspects of these spaces, giving rise to series of questions in this area.
Bhagwat, C., Pisolkar, S. and Rajan, C.S. (2013). Commensurability and representation equivalent
arithmetic lattices. International Mathematical Research Notices doi: 10.1093/imrn/rns282.
Hogadi, A. and Pisolkar, S. (2013). An equicharacteristic analogue of Hesselholt’s conjecture on
cohomology of Witt vectors. Acta Arithmetica 158(2):165-171.
Hogadi, A. and Pisolkar, S. (2011). On the cohomology of Witt vectors of p-adic integers and a
conjecture of Hesselholt. Journal of Number Theory 131(10):1797-1807.
Pisolkar, S. (2008). The Chow group of zero-cycles on certain Châtelet surfaces over local fields.
Indagationes Mathematicae 19(3):427-439.
Low Dimensional Topology
My area of research is low-dimensional topology. This is a very active area of
research with several longstanding conjectures proved fairly recently, like
Thurston’s Geometrization conjecture (which implies the Poincare conjecture)
and the Virtual Fibering conjecture. Within low-dimensional topology I focus
mainly on foliations, triangulations and Heegaard splittings of 3-dimensional
manifolds.
Tejas Kalelkar
Assistant Professor
[email protected]
After completing his MSc from
Indian Institute of Technology,
Bombay, Tejas Kalelkar got his
PhD from Indian Statistical Institute,
Bangalore in 2010. He was then a
postdoctoral fellow at Institute of
Mathematical Sciences, Chennai
and a Chauvenet Postdoctoral
Fellow at the Washington University
in St Louis, USA. He joined IISER
Pune in December 2013.
A closed book looks like a solid 3-dimensional object, but on closer analysis is
observed to consist of 2-dimensional pages stacked tightly together. Similarly,
every 3-manifold can be built by stacking 2-dimensional surfaces tightly together
into what is called a foliation. I am studying a special class of foliations called taut
foliations which tell us useful topological properties of the 3-manifold.
On cutting open a 3-manifold along a special embedded surface, called the
Heegaard-splitting surface, we end up with two simple pieces called
handlebodies. Every closed 3-manifold has such a splitting surface which may
not be unique. I am currently working on a structure for these splitting surfaces
when a 3-manifold has infinitely many of them.
Every 3-manifold can be built by suitably sticking tetraheda together. Normal
surfaces are surfaces embedded particularly `nicely' with respect to such a
triangulation. I have proved several results using normal surfaces, such as a
weak converse of Haken’s well-known result about normality of incompressible
surfaces with respect to every triangulation of the 3-manifold.
Kalelkar, T. and Roberts, R. Taut foliations in surface bundles with multiple punctures.
arXiv:1211.3637, Pacific Journal of Mathematics 273:257-275.
Gadgil, S. and Kalelkar, T. (2013). A Chain complex and Quadrilaterals for normal surfaces. Rocky
Mountain Journal of Mathematics, 43(2):479-487.
Kalelkar, T. (2009). Incompressibility and normal minimal surfaces. Geometriae Dedicata 142(1):6170.
Kalelkar, T. (2008). Euler characteristic and quadrilaterals of normal surfaces. Proceedings of the
Indian Academy of Sciences Mathematical Sciences 118(2):227-233.
Statistics
My research interests are in the areas of inference in stochastic processes,
survival analysis reliability theory and statistics in finance. Currently I am working
on two problems.
Uttara NaikNimbalkar
Visiting Faculty
[email protected]
Uttara Naik-Nimbalkar joined IISER
in February 2015. She has about
thirty years of teaching and
research experience at the
University of Pune with visiting
positions at the Michigan State
University, the University of
Edinburgh and University of
Waterloo.
(i) Modeling and analysis of statistical dependence: for example, in load sharing
systems the failure of a component may reduce (increase) the lifetimes of the
surviving components resulting in dependence between their lifetimes. (ii)
Hypothesis testing problems in competing risks with missing causes of failure: the
failure of a unit is caused by one of the several risks acting on it. It is of interest to
know whether some risk dominates the others but sometimes the actual cause of
failure for some units is missing.
Sutar, S.S. and Naik-Nimbalkar, U.V. (2014). Accelerated failure time models for loadsharing
systems. IEEE Transactions on Reliability 63(3):706-714.
Deshpande, J.V., Dewan, I. and Naik-Nimbalkar, U.V. (2010). A family of distributions to model load
sharing systems. Journal of Statistical Planning and Inference 140(6):1441-1451.
Lam, K.F., Deshpande, J.V., Lau, E.H., Naik-Nimbalkar, U.V., Yip, P.S. and Xu, Y. (2009). A test for
constant fatality rate of an emerging epidemic, with applications to the SARS syndrome in Hong
Kong and Beijing. Biometrics 64(3):869-876.
Abegaz, F. and Naik-Nimbalkar, U.V (2008). Modeling statistical dependence of markov chains via
copula models. Journal of Statistical Planning and Inference 138(4):1131-1146.
Algebraic Geometry
My research can be divided into three categories: intersection theory, derived
categories, and T-varieties.
Intersection theory
In intersection theory, one defines invariants of algebraically defined geometric
spaces in terms of how the spaces lying on the given space intersect each other.
One can study those invariants to determine deep geometric properties of the
space.
Vivek Mohan
Mallick
Assistant Professor
[email protected]
After completing BStat (1999) and
MStat (2001) from Indian Statistical
Institute, Vivek Mallick got his PhD
Research (TIFR) Mumbai, India in
2008. He has joined IISER Pune in
2012 after completing his
postdoctoral research at the
Institute of Mathematical Sciences
in Chennai and Centre de Recerca
Matematica in Barcelona, Spain.
Derived category
Given a variety (a type of algebraically define geometric space), one can define
another algebraic object called derived category. It is known that a lot of the
geometric properties of the space translate to algebraic properties of the derived
category.
T-variety
While studying an object one many times first determine its group of symmetries.
The same holds for varieties. When the group of symmetries contain a torus, one
can, with some additional hypothesis describe a variety purely in terms of some
combinatorial data. Currently I am working on such varieties.
Dubey, U.V. and Mallick, V.M. (2012). Reconstruction of a superscheme from its derived category.
Journal of the Ramanujan Mathematical Society 27(4).
Dubey, U.V., Mallick, V.M. (2012). Spectrum of some triangulated categories. Journal of Algebra
364:90-118.
Mallick, V.M. (2009). Roitman's theorem for singular projective varieties in arbitrary characteristic.
Journal of K-Theory 3:501-531.
Adjunct Faculty Members
SA Katre
Professor & Head
Department of Mathematics
University of Pune, Pune
E-mail: [email protected]
[email protected]
SA Katre received Masters degree in Mathematics from University of Pune and
PhD from Panjab University, Chandigarh, India. He began his academic career
from SP College of Pune and moved to University of Pune in 1988 as a faculty
member and has been there since. Prof Katre’s work is in the area of Algebra
and Number Theory, in particular, cyclotomy, number of points on curves over
finite fields, Waring's problem for matrices, coding theory, and group theory. His
pedagogical interests include contributing to mathematics olympiads, open
source mathematical software, and e-learning in mathematics. Prof Katre had
served as the editor of pedagological journal Bona Mathematica and has
organized the NBHM sponsored ATM Schools in Mathematics during 2004-2012.
Sujatha Ramdorai
Canada Research Chair, Department of Mathematics
University of British Columbia, Canada
Sujatha Ramdorai obtained her PhD in TIFR/Bombay University in 1992 and was
with TIFR till January 2012. She currently holds a Canada Research Chair at the
Department of Mathematics, University of British Columbia. Her research
interests include Iwasawa theory and the theory of motives. Prof Ramdorai is a
recipient of the Shanti Swarup Bhatnagar Award and the ICTP Ramanujan
Award. She was a Member of the National Knowledge Commission and is a
Member of the Scientific Advisory Council to the Prime Minister, and also the
National Innovation Council. She is also interested in broader educational issues
and in policy matters related to Higher Education and Research.
Postdoctoral Fellows
Amlan Barua
Postdoctoral Research Associate (till January 2015)
Amlan’s research work focuses primarily on the numerical solution of partial differential equations that are
encountered in different fields of applications. Earlier, he had worked on problems of Materials Science where
his task was to find effective solvers for boundary integral equations. More lately, he has developed an interest
in the field Bio-Mathematics. With Dr Pranay Goel at IISER Pune, Amlan was working on several research
projects ranging from clinical biology to numerical simulation of partial differential equations that emerge from
the modeling of Islets of Langerhans. Apart from applied mathematics, he is also interested in functional
analysis and theoretical partial differential equations. Amlan is presently working as a Development Engineer
with Comsol Multiphysics in Bangalore.
Barua, A., Li, S., Feng, H. and Li, X. (2013). An efficient rescaling algorithm for simulating the evolution of multiple elastic precipitates.
Communications in Computational Physics 14(4):940-959.
Feng, H., Barua, A., Li, S. and Li, X. (2013). A parallel adaptive treecode algorithm for evolution of elastically stressed solids. Communications in
Computational Physics 15(2):365-387.
Bhakti Bhushan Manna
Postdoctoral Research Associate
Bhakti did his PhD from TIFR-CAM Bangalore. His area of research is partial differential equation. He has
completed the degree on December 2014 under the guidance of Prof PN Srikanth. He has joined IISER Pune
as a Post doctoral Research Associate (PRA) on March 1, 2015. His thesis work involved mainly two classes
of problems: First one concerning concentrating solutions and the other on the so-called problem of
resonance. Singularly perturbed elliptic equations have been a great interest in PDE for last two decades. And
his focus has been on finding solutions with higher dimensional concentrations. He is also interested in finding
the existence results for the classical resonance problem which has been partly answered in one of their
recent works.
Manna, B.B. and Srikanth, P.N. (2015). On a problem of resonance with exponential nonlinearity. Journal of Mathematical Analysis and
Applications 421(2):1603-1615.
Manna, B.B. and Srikanth, P.N. (2014). On the solutions of a singular elliptic equation concentrating on a circle. Advances in Nonlinear Analysis
3(3):141-155.
Manna, B.B. and Srikanth, P.N. (2014). On the solutions of a singular elliptic equation concentrating on two orthogonal spheres. Nonlinear
Differential Equations Applications NoDEA 21(6):915-927.
Manna, B.B. and Santra, S. On a superlinear Ambrosetti Prodi problem: Interior concentration on geodesics (preprint).
Chitrabhanu Chaudhuri
Chitrabhanu did his PhD in Mathematics from Northwestern University 2007-2013 and was a postdoctoral
fellow at Max Plank Institute for Mathematics (2013-2014) before joining IISER Pune. His research revolves
around the topology and geometry of the Moduli of Curves over Complex numbers. The Moduli Space of
Curves parameterize algebraic curves or Riemann surfaces, up to isomorphisms. It has been a central topic in
mathematical research for several decades and brings various fields of mathematics together, for example
Algebraic Geometry, Geometric Group theory and Teichmüller theory. It has important connections with
physics as well. There are mainly two directions of research that Chitrabhanu has pursued: one roughly
concerns finding some bounds on the topological complexity of certain partial compactifications on the Moduli
of genus g curves. This involves computing certain cohomology groups; and the other line of research is about
certain geometrically relevant subrings of the cohomology ring of the Moduli space known as the Tautological
ring.
The Cohomological Excess of Certain Moduli Spaces of Curves of Genus g. International Mathematical Research Notices IMRN (2013).
Topological Bounds on Certain open Subvarieties of the Compactified Moduli space of Curves; PhD thesis, Northwestern University 2013.
Equivariant Polynomial of certain Moduli of Weighted Pointed Rational Curves (In preparation)
Postdoctoral Fellows
Dipramit Majumdar
Dipramit Majumdar obtained his PhD from Brandeis University, USA in 2013. He was a visiting scientist in ISI
Bangalore from 2013-2014 before joining IISER Pune in 2014. Dipramit's research interest lies in number
theory. Even though he is sometimes intrigued by elementary number theoretic problems such as Class
Groups and Diophantine equations, his main research interest lies in p-adic families of modular forms.
Modular forms are certain functions on the complex upper half planes with a lot of symmetries. To a modular
form one can associate certain object called the L-function. One of the most promising ways to understand
classical modular forms and their associated L-function is via study of their p-adic analogue. Study of p-adic
modular forms was initiated by Serre, later Hida and then Coleman-Mazur constructed p-adic familes of 'nice'
modular forms, called Hida family and eigencurve respectively. These objects plays crucial role in
understanding and solving many problems in number theory, for example, key step in Mazur-Wiles proof of
Iwasawa main conjecture for rational numbers is understanding geometry of the eigencurve at certain points.
Majumdar, D. Geometry of the eigencurve at critical Eisenstein series of weight 2. To appear in Journal de Théorie des Nombres de Bordeaux.
Majumdar, D. Endoscopic transfer between eigenvarieties of definite unitary groups (Submitted)
Kulkarni, M., Majumdar, D. and Balasubramanian, S. l-Class groups of cyclic extensions of prime degree l (Submitted)
Graduate Students,
BS MS Project Students & Teaching Assistants
Advait Phanse
Girish Kulkarni
Graduate Student
Graduate Student
Advait has completed MSc from Sir
Parshurambhau College in July
2014 and joined IISER Pune in
August 2014. Presently he is doing
PhD program related course work.
Girish completed MSc Mathematics
from IIT Madras in 2010 and MSc
from University of Western Ontario,
Canada in 2012. Girish joined IISER
Pune in 2013. In December 2014 he
attended Advanced Instructional
School on Schemes and
Cohomology and has done minor
thesis under the guidance of Prof
Tejas Kalelkar. He is working toward
PhD with the guidance of Dr Amit
Hogadi. Girish’s expository article
has appeared recently (Representation
Theory and Particle Physics, Forays-14
Souvenir 55-56).
Ayesha Fatima
Gunja Sachdeva
Ayesha completed her BS-MS from
IISER Pune in 2012 before joining
the PhD program in August 2013.
She has since completed her
course work and is
currently reading about Lie
Algebras with Dr Bhagwat. Her
interest lies in Number Theory and
Representation Theory.
Gunja completed MPhil in
Mathematics from Dayalbagh
Educational Institute, Deemed
University, Agra in December 2011
and joined IISER Pune in August
2012. She is currently working
toward PhD under the guidance of
Prof A Raghuram in the area of
Number Theory.
Chaitanya Ambi
Hitesh Raundal
Chaitanya completed his MSc from
IIT Kharagpur in 2009. He joined
IISER Pune in August 2013 as a
Project Fellow. He is a PhD student
now and is completing the course
work.
Hitesh obtained MSc in Applied
Mathematics from the University of
Hyderabad and joined IISER Pune
in January 2011. He is a graduate
student with Dr Rama Mishra in the
area of knot theory. He has been
working on the minimal polynomial
representations of knots and their
super bridge indices, and trying to
build relation between various
numerical knot invariants particularly
polynomial degree, edge number
and super bridge index of knots.
Debangana Mukherjee
Jyotirmoy Ganguly
Debangana has completed her MSc
from Mount Carmel College (under
Bangalore University) in 2013 and
joined IISER Pune soon after as a
graduate student and has completed
a one year coursework as a part of
the Mathematics PhD program. She is
currently reading in the area of elliptic
partial differential equations under the
guidance of Dr Mousomi Bhakta.
Jyotirmoy completed MSc in
Mathematics from University of
Hyderabad in 2013 and joined
IISER Pune soon after. He has
completed a one year course work
as a part of the Mathematics PhD
program at IISER Pune. His
research interest is in
Representation Theory of Lie
groups.
Graduate Student
Graduate Student
Graduate Student
Graduate Student
Graduate Student
Graduate Student
Makarand Sarnobat
Prabhat Kushwaha
Makarand completed MSc in
Mathematics from Sir
Parshurambhau College, Pune in
2012 and joined IISER Pune
immediately after that. He is
working with Prof Raghuram toward
PhD in the area of algebraic
number theory and representations
theory. Makarand has been a
teaching assistant for these
courses: Introduction to Proofs;
Linear Algebra; Multivariable
Calculus; and Complex Analysis.
He has attended a conference on
Lie Groups and Lie Algebras in IIT
Bombay in July 2014.
Prabhat completed MSc from the
Department of Mathematics, Banaras
Hindu University, Varanasi and joined
IISER Pune in January 2012. He has
successfully completed all the
requirements by the Institute viz. course
work, comprehensive exams and minorthesis. Prabhat is currently working with
Dr Ayan Mahalanobis his broad area of
research is public key cryptography.
Manidipa Pal
Pralhad Shinde
Manidipa joined IISER Pune in
January 2012. She has completed
course work, comprehensive exams
and minor thesis, which are
in partial fulfillment of PhD program.
Her minor thesis was carried out
with guidance from Chandrasheel
Bhagwat. Manidipa’s is now
working with Dr Baskar
Balasubramanyam in the area of
algebraic number theory.
Pralhad completed Masters in
Mathematics in 2011 from University of
Pune, Pune and joined IISER Pune in
January 2012. He is working with Dr
Ayan Mahalanobis and Dr Anupam
Singh in the areas of cryptography and
computational group theory.
Milan Kumar Das
Rashmi Kulkarni
Milan completed MSc from
Vidyasagar University, West Bengal
in 2012. He joined IISER Pune in
August 2013.
Rashmi obtained MSc in Microbiology
from MS University, Baroda and an
MTech from the Centre for Modeling
and Simulation, University of Pune,
Pune. She joined IISER Pune in August
2010 and is working with Dr Pranay
Goel toward her PhD. Her research
involves quantitating oxidative stress in
the development of insulin resistance.
Neha Prabhu
Rohit Joshi
Neha completed her MSc in
Mathematics from IIT Bombay and
joined IISER Pune in August 2012.
She is currently working toward
PhD under the guidance of Dr
Kaneenika Sinha. Her interests lie
in number theory and
representation theory.
Rohit has a Masters degree from IIT
Kanpur. He has completed course work
and cleared comprehensive exams
toward IISER Pune’s PhD program in
Mathematics and is currently working
with Dr Steven Spallone. He was the
winner of silver medal in International
Mathematics Olympiad in 2004 while in
his 12th standard and was chosen as
the IISER Pune Mathematics Student of
the Year in 2013.
Graduate Student
Graduate Student
Graduate Student
Graduate Student
Graduate Student
Graduate Student
Graduate Student
Graduate Student
Sudhir Pujahari
Akash Krishna
Sudhir obtained MSc in
Mathematics from Utkal University,
Orissa. He joined IISER Kolkata in
January 2011 as a CSIR JRF and
shifted to IISER Pune in December
2012. He is working with Dr
Kaneenika Sinha in the area of
Analytic Number Theory. Some of
his work has been accepted for
publication (with Meher, J. and
Akash is currently working on his BS
MS thesis with Dr Anindya Goswami.
His thesis studies option pricing
problem in a market model where semiMarkov switching of the parameters is
considered in a Levy process dynamics.
Sushil Bhunia
K Hariram
Sushil completed MSc
(Mathematics) in 2010 from
Jadavpur University, Kolkata, India.
He joined IISER Pune in January
2012 and completed course work
along with comprehensive
examinations that are part of the
graduate program. Sushil is
presently working with Dr Anupam
Singh on algebraic groups.
Hariram is doing his fifth year project
with Dr Ayan Mahalanobis. He is
studying how to solve the discrete log
problem using Function field sieve for
index calculus-in particular, a new
method to improve the sieving step
called pinpointing which reduces the
computation time significantly. He is
also investigating whether this
improvement can be adopted for other
similar problems like integer
factorization.
Tathagata Mandal
Nishad Mandlik
Tathagata completed his MSc in
Mathematics from Visva-Bharati
University, Santiniketan, India in
2012. He joined IISER Pune in
August 2013. He is presently doing
coursework as a part of the
Mathematics PhD program at
IISER Pune and is interested in
Number Theory and Algebraic
Geometry.
Nishad is working on his fifth year thesis
project with Dr Rabeya Basu. The topic
of his project is 'K-Theory: Completion
of Unimodular Rows.' He is using the
software 'Singular' to replicate a result
on the completion of unimodular rows of
length 3. Nishad is also interested in
math and science education.
Yasmeen Akhtar
Preeti
Yasmeen completed MSc in
Mathematics from University of
Pune and joined IISER Pune in
January 2011. She is working
toward her PhD with Dr Soumen
Maity in the area of combinatorics
and graph theory. Recent Publications:
Preeti is currently working on her BS
MS fifth year project with Dr Ayan
Mahalanobis on Secret sharing
schemes and its various applications.
This topic uses Lagrange interpolation
in finite fields and has many
applications in real life. Notable ones
are e-voting and secure multiparty
computations.
Graduate Student
BS MS Student
Shankhadhar, K.D.; Sign changes of
coefficients of certain Dirichlet series
Functiones Et Approximatio Commentarii
Mathematici).
Graduate Student
Graduate Student
Graduate Student
Akhtar, Y., Maity, S. and Chandrasekharan,
R.C. Covering Arrays of Strength four with
budget constraints. Mathematical and
Computational Sciences 106-114, Narosa
Publishing; Akhtar, Y., Maity, S. and
Chandrasekharan, R.C. Covering arrays of
strength four and software testing. Springer
Proceedings in Mathematics and Statistics (To
appear).
BS MS Student
BS MS Student
BS MS Student
Reshma
Chandrasekharan
BS MS Student
Reshma is working toward her BS
MS fifth year project with Dr
Soumen Maity on the topic
"Construction of covering arrays".
She likes programming and is
interested in developing tools for
solving mathematical problems.
Publications: Chandrasekharan, R.C. and
Maity, S. Covering Arrays of Strength Two and
Pair wise Software Testing, Mathematical and
Computational Sciences, Narosa, 2015, 115121; Akthar, Y., Maity, S. and
Chandrasekharan, R.C. Covering Arrays of
Strength Four and Software Testing, Springer
Proceedings in Mathematics and Statistics (To
appear).
Aman Jhinga
Teaching Assistant
Aman graduated with BSc (Hons)Maths and Computing degree in June
2010 and MSc (Mathematics) degree in
June 2012 from Panjab University,
Chandigarh. She has assisted Dr Amit
Hogadi in conducting Single Variable
Calculus course, Dr Steven Spallone for
Introduction to Proofs and Dr Baskar
Balasubramanyam for Linear Algebra
for fall semester 2014. Aman is
currently assisting Dr Soumen Maity in
conducting Probability & Statistics
course, Dr Debargha Banerjee for
Multivariable Calculus and Dr Collins
Assisi in conducting Introduction to
Computation course for Spring
semester 2015. She is also doing a
reading project with Dr Steven Spallone
on p-adic numbers.
Sanket Nandan
Jatin Majithia
Sanket is doing his project on
Statistical inference of semiMarkov process and application in
finance with Dr Anindya Goswami.
Jatin has an MSc in Mathematics
degree from University of Pune and is
presently assisting with teaching at
IISER Pune.
Shirish Kulhari
Uday Jagadale
Shirish is working with Dr Anindya
Goswami toward his BS MS fifth
year project. The title of his
research project is “Implied
Volatility in a Regime Switching
Market: Theory and Computation”.
Uday has completed MSc from the
Department of Mathematics, University
of Pune in 2014 and joined IISER Pune
as a Teaching Assistant. He has
assisted Dr Amit Hogadi and Dr Steven
Spallone for courses on Calculus of
One Variable and Introduction to Proofs
respectively. Currently he is a teaching
assistant for these courses: Calculus of
multivariable (taught by Dr Debargha
Banerjee); and Probability and Statistics
(taught by Dr Soumen Maity).
BS MS Student
BS MS Student
Shiva Chidambaram
BS MS Student
Shiva is currently working on his fifth
year project with Prof A Raghuram on
Cohomology of GL(2). The goal of this
project is to understand, in the language
of automorphic forms of GL(2,F) for a
number field F, the sheaf cohomology of
a sheaf of vector spaces defined on a
locally symmetric space attached to
GL(2,F) from a highest weight
irreducible representation of it. A
specific goal is to understand the inner
cohomology. He is also a Teaching
Assistant for the course Multivariable
Calculus taught by Dr Debargha
Banerjee and Dr Anup Biswas.
Teaching Assistant
Teaching Assistant
Support Staff
Kalpesh Pednekar
Office Assistant
Kalpesh Pednekar completed his Bachelor Degree in Commerce from University of Mumbai. He joined IISER
Pune in March 2013 and is presently assisting Mathematics group in various administrative responsibilities in
addition to assisting the Physics Group at IISER Pune.
R Bhagyalaxmi
Office Assistant
Bhagyalaxmi completed her BSc from Osmania University, Hyderabad. Microbiology, Chemistry and
Computer Applications were the subjects of her study in BSc. She also completed her MSc in Computer
Science from Annamalai University, Tamilnadu. She joined IISER Pune in December 2014 and is providing
administrative support to the Mathematics group.
Suvarna Gharat
Office Assistant
Suvarna completed her BSc in Physics from Fergusson College and her post-graduation from Modern
College, Pune. She joined IISER Pune in July 2011 and is presently assisting the Mathematics group in
various administrative responsibilities.
Publications
2015
Akhtar, Y., Chandrasekharan, R.C. and Maity, S.- Covering Arrays of Strength Four and Software
Testing. Springer Proceedings in Mathematics & Statistics (Accepted)
Akhtar, Y., Chandrasekharan, R.C. and Maity, S.- Covering Arrays of Strength four with budget
constraints. Mathematical and Computational Sciences 106-114, Narosa Publishing House, 2015.
Banerjee, D. and Raghuram, A. - p-adic L-functions for GL_n (Submitted)
Banerjee, D. and Krishnamoorthy, S.- The Eisenstein elements inside the modular symbols for product of
two distinct primes (Submitted)
Barua, A.; Goel, P. - The lattice origin of small-world networks in pancreatic tissues. (Submitted)
Bhakta, M. - Entire solutions for a class of elliptic equations involving p-biharmonic operator and Rellich
potentials. Journal of Mathematical Analysis and Applications 423 (2015), no. 2, 1570-1579.
Bhunia, S., Mahalanobis, A. and Singh, A.- Gaussian Elimination in Symplectic and Split Orthogonal
groups (Submitted)
Chandrasekharan, R.C. and Maity, S.- Covering Arrays of Strength Two and Pairwise Software Testing.
Mathematical and Computational Sciences 115-121, Narosa Publishing House, 2015.
Chaudhuri, C.- The Cohomological Excess of Certain Moduli Spaces of Curves of Genus g. International
Mathematics Research Notices 4 (2015) 1056-1074.
Goswami, A., Patel, J. and Sevgaonkar P.- The optimal hedging in a semi-Markov modulated market
(Submitted)
Kalelkar, T. Roberts, R.- Taut foliations in surface bundles with multiple boundary components. Pacific
Journal of Mathematics Vol No. 273 (2015) 257-275.
Mahalanobis, A., Singh, A.- The MOR cryptosystem and unitary group in odd characteristic. (Submitted)
Kulkarni, M., Majumdar, D. and Sury, B.- l-class groups of cyclic extensions of prime degree l. The
Journal of the Ramanujan Mathematical Society (Accepted)
Mishra, R. and Raundel, H. - Spaces of polynomial knots in low degree (Submitted)
2014
Balasubramanyam, B. and Majumdar, D.- Ordinary families over definite unitary groups (Submitted)
Balasubramanyam, B. and Raghuram, A.- Special values of adjoint L-functions and congruences for
automorphic forms on GL(n) over a number field (Submitted)
Banerjee, D.- A note on the Eisenstein elements for prime square level. Proceedings of the American
Mathematical Society 142 (2014), 3675-3686.
Banerjee, D. - Differential modular forms on the Shimura curves over totally real fields. Journal of
Number Theory 135 (2014), 353-373.
Basu, R.- Local-global principle for quadratic and Hermitian groups and the nilpotence of KH1 (Submitted)
Bhagwat, C.- On Deligne's periods for tensor product motives. Comptes rendus - Mathématique DOI:
10.1016/j.crma.2014.11.016.
Bhakta, M.- Infinitely many sign changing solutions of an elliptic problem involving critical Sobolev and
Hardy-Sobolev exponent (Submitted)
Bhakta, M.- Caffarelli-Kohn-Nirenberg type equations of fourth order with the critical exponent and Rellich
potential (Submitted)
Bhakta, M.- Semilinear elliptic equation with biharmonic operator and multiple critical nonlinearities.
Advanced Nonlinear Studies (Accepted)
Bhakta, M. and Marcus, M. - Semilinear elliptic equations admitting similarity transformations. Journal of
Functional Analysis Vol 267 (2014), no. 10, 3894-3930.
Bhakta, M. and Marcus, M.- Reduced limit for semilinear boundary value problems with measure data.
Journal of Differential Equations Vol 256 (2014), no. 8, 2691-2710.
Arapostathis, A., Biswas, A. and Pang, Guodong - Ergodic control of multi-class M/M/N+M queues in the
Halfin-Whitt regime . Annals of Applied Probability (Accepted)
Atar, R., Biswas, A., Kaspi, H.- Fluid limits of G/G/1+G queues under non-preemptive Earliest-DeadlineFirst discipline . Mathematics of Operation Research (Accepted)
Biswas, A.- Risk-sensitive control for the multiclass many-server queues in the moderate deviation
regime. Mathematics of Operation Research 39 (2014), no. 3, 908-929.
Atar, R. and Biswas, A.- Control of the multiclass G/G/1 queue in the moderate deviation regime. Annals
of Applied Probability 24 (2014), no. 5, 2033-2069.
Chorwadwala, A. and Mahadevan, R.- A shape optimization problem for the $p$-Laplacian. Proceedings
of the Royal Society of Edinburgh (Accepted)
Chorwadwala, A., Mahadevan, R. and Toledo, F. - On the Faber-Krahn Inequality for the Dirichlet $p$Laplacian. ESAIM:Control, Optimization and Calculus of Variations; Cambridge Journal (2014)
DOI:10.1051/cocv/2014017.
Deshpande, J., Lam, K.F., Naik-Nimbalkar, U.V. and Xu, Y.- Tests for comparing the progression of an
epidemic in two groups. Journal of Indian Statistical Association (Accepted)
Dwivedi, A. (Sponsor: Goel, P.) - A Stochastic Version of the Pedersen-Sherman Insulin Secretion Model.
SIAM Undergraduate Research Online (SIURO) Published electronically Vol. 7. (2014)
http://dx.doi.org/10.1137/12S011994.
Goswami, A. and Saini, R.K. - Volterra equation for pricing and hedging in a regime switching market.
Cogent Economics and Finance 2(2014), no.1, 1-11.
Atar, R., Shwartz, A. and Goswami, A.- On the risk-sensitive cost for a Markovian multiclass queue with
priority. Electronic Communications in Probability 19 (2014), no. 11, 1-13.
Kaipa, K.- An asymptotic formula in q for the number of [n,k] q-ary MDS codes. IEEE Transactions on
Information Theory Vol PP, Issue 99 (early access).
Kaipa, K.- An asymptotic formula in q for the number of [n,k] q-ary MDS codes. IEEE Transactions on
Information Theory 60 (2014), no. 11, 7047-7057.
Majumdar, D.- Endoscopic transfer between eigenvarieties for definite unitary groups (Submitted)
Majumdar, D.- Geometry of the eigencurve at critical Eisenstein series of weight 2. Journal de Théorie
des Nombres de Bordeaux (Accepted)
Sebastian, R. - Examples of smash nilpotent cycles on rationally connected varieties (Submitted)
Colloquia & Seminars
Colloquia
Speaker
Date
Title of the Talk
Prof Nitin Nitsure
TIFR, Mumbai
Mar 13, 2015
Euclidean Geometry and Physics
Dr Abhishek Banerjee
IISc Bangalore
Feb 27, 2015
Hecke operators on Line bundles over Modular curves
Dr Chitrabhanu Chaudhary
IISER Pune
Jan 23, 2015
Operads and Moduli of Curves
Prof L Mahadevan
Harvard University
Jan 09, 2015
Of flags and fishes
Prof Michel Waldschmidt
Institut de Mathématiques de Jussieu,
Paris VI
Dec 18, 2014
Continued fractions : Introduction and applications
Dr Manoj Kumar Yadav
HRI, Allahabad
Dec 05, 2014
Automorphisms of groups preserving conjugacy classes
Prof Siegfried Boecherer
Universität Mannheim, Germany
Oct 31, 2014
Siegel modular forms mod p
Dr Anupam Kumar Singh
IISER Pune
Oct 17, 2014
Word problem in finite classical Chevalley groups
Dr Tejas Kalelkar
IISER Pune
Sep 19, 2014
Incompressible surfaces and normality in 3-manifolds
Dr Joël Riou
Université Paris-Sud, France
Aug 22, 2014
Purity and duality in étale cohomology (after O. Gabber)
Dr Raghav Kulkarni
Centre for Quantum Technologies
Aug 04, 2014
Decision Trees, Evasiveness, Solvable Groups, and
Music of Primes
Prof Jeffrey Adler
American University
Jul 24, 2014
Representation Theory and p-adic Numbers: What and
Why
Dr Moira Chas
Stonybrook University
Jul 11, 2014
The Goldman Bracket on Surfaces
Prof Steven Weintraub
Lehigh University
Jul 07, 2014
The adjoint of differentiation
Prof Mahan Maharaj
RKM Vivekananda University, Belur
Math
Jun 06, 2014
3-manifolds and (quasi)projective varieties
Dr Shanta Laishram
ISI Delhi
May 02, 2014
Grimm's Conjecture and Smooth Numbers
Prof Uttara Naik-Nimbalkar
University of Pune
Apr 25, 2014
Statistical tests for comparing the fatality of an epidemic
in two groups
Prof CS Aravinda
TIFR-CAM, Bangalore
Apr 11, 2014
Dynamics of geodesic conjugacies
Prof Parameswaran Sankaran
IMSC-Chennai
Apr 04, 2014
Twisted conjugacy in R. Thompson's groups
Prof Amitava Bhattacharya
TIFR, Mumbai
Mar 21, 2014
Existence problems in Set Systems
Dr Stefan Friedl
University of Regensburg
Mar 14, 2014
The profinite completion of knot groups
Prof MS Narasimhan
IISc, Bangalore
Mar 08, 2014
Mathematical Research in India after Independence:
The early years
Prof Ravi Ramakrishna
Cornell University
Mar 07, 2014
Galois Representations
Algebraic Geometry Seminars
Speaker
Date
Title of the Talk
Prof Kapil Hari Paranjape
IISER, Mohali
Mar 04, 2015
The work of Grothendieck: Some aspects of his work
Prof Kapil Hari Paranjape
IISER, Mohali
Mar 03, 2015
Lindel's theorem: A Vector bundle on X x A^1 comes
from X
Analysis Seminars
Speaker
Date
Title of the Talk
Dr M Ashok Kumar
Indian Institute of Science, Bangalore
Feb 25, 2015
Statistical inference based on a parametric family of
divergences
Dr Amogh Deshpande
University of Liverpool,UK
Jan 7, 2015
On the role of Follmer-Schweizer minimal martingale
measure in risk sensitive control asset management
Dr Ronnie Sebastian
IISER Pune
Nov 07, 2014
Bounded Hermitian Operators and Schur's lemma
Dr Ronnie Sebastian
IISER Pune
Oct 31, 2014
Bounded Hermitian Operators and Schur's lemma
Dr Anisa Chorwadwala
IISER Pune
Oct 24, 2014
Geometric overview of Symmetric Spaces
IISER Pune
Oct 17, 2014
Geometric overview of Symmetric Spaces
Dr Rahul Garg, Technion
Israel Institute of Technology
Oct 14, 2014
The lattice point counting problem on the Heisenberg
groups
IISER Pune
Oct 10, 2014
Geometric Overview of Symmetric Spaces
Dr Supriya Pisolkar
IISER Pune
Sept 26, 2014
Representation of SL2(R)
Dr Debdip Ganguly
TIFR-CAM, Bangalore
Sept 25, 2014
Partial Differentiation Equation on Hyperbolic Space
Dr Supriya Pisolkar
IISER Pune
Sept 19, 2014
Dr Chandrasheel Bhagwat
IISER Pune
Sept 12, 2014
IISER Pune
Aug 29, 2014
Dr Ronnie Sebastian
IISER Pune
Aug 20, 2014
Representation theory of topological groups, PeterWeyl Theorem for compact groups
Mr Souvik Roy
TIFR-CAM, Bangalore
Jun 05, 2014
A Vorticity-Velocity Formulation for Incompressible 2-D
Euler Flows using Discontinuous Finite Element
Methods
Dr Supriya Pisolkar
IISER Pune
Jun 04, 2014
Analysis Lecture Series on Representation Theory and
Linear Lie Groups (Lecture XV)
Dr Supriya Pisolkar
IISER Pune
Jun 03, 2014
Linear Lie Groups (Lecture XIV)
Dr Supriya Pisolkar
IISER Pune
May 30, 2014
Linear Lie Groups (Lecture XIII)
IISER Pune
May 22, 2014
Linear Lie Groups (Lecture XII)
IISER Pune
May 20, 2014
Linear Lie Groups (Lecture XI)
IISER Pune
May 15, 2014
Linear Lie Groups (Lecture X)
Ms Neha Prabhu
IISER Pune
May 13, 2014
Linear Lie Groups (Lecture IX)
IISER Pune
May 06, 2014
Linear Lie Groups (Lecture VIII)
IISER Pune
Apr 29, 2014
Linear Lie Groups (Lecture VII)
Prof Raju George
IIST Thiruvantapuram
Apr 21, 2014
Controllability of Systems Described by Differential
Equations Using Tools of Functional Analysis
IISER Pune
Apr 18, 2014
Linear Lie Groups (Lecture VI)
IISER Pune
Apr 16, 2014
Linear Lie Groups (Lecture V)
Dr Apala Majumdar
University of Bath
Apr 11, 2014
Biaxial defect cores in nematic equilibria: an asymptotic
result
Prof CS Aravinda
TIFR-CAM, Bangalore
Apr 10, 2014
Homotopy type and volume of locally symmetric spaces
IISER Pune
Apr 09, 2014
Linear Lie Groups (Lecture IV)
Dr Supriya Pisolkar
IISER Pune
Apr 02, 2014
Linear Lie Groups (Lecture III)
Dr Supriya Pisolkar
IISER Pune
Mar 26, 2014
Linear Lie Groups (Lecture II)
Dr Praveen C
TIFR-CAM, Bangalore
Mar 25, 2014
Kinetic schemes for convection-diffusion and NavierStokes equations
Dr Supriya Pisolkar
IISER Pune
Mar 19, 2014
Linear Lie Groups (Lecture I)
Prof Gopal Basak
ISI Kolkata
Mar 07, 2014
Diffusion Approximation to Adaptive MCMC
Number Theory Seminars
Date
Title of the Talk
Dr Jonathan Huang
University of Maryland
Mar 09, 2015
Higher Fitting ideals and the structure of ideal class
groups
Dr Debargha Banerjee
IISER Pune
Mar 02, 2015
Eisenstein ideals
Dr Steven Spallone
IISER Pune
Feb 20, 2015
Weyl's Law: Euclidean Case
IISER Pune
Feb 16, 2015
Eisenstein ideals
Dr Steven Spallone
IISER Pune
Feb 13, 2015
Weyl's Law: Euclidean Case
Dr Chandrasheel
Bhagwat
IISER Pune
Feb 06, 2015
Trace formula and its applications in isospectrality
problems
Dr Supriya Pisolkar
IISER Pune
Jan 30, 2015
Trace Formula
Dr Steven Spallone
IISER Pune
Jan 19, 2015
Trace Formula
Dr Florian Sprung
Princeton Univerity
Jan 15, 2015
Rational points of modular abelian varieties in towers of
number fields: How to bound the rank.
Dr Abhishek Saha
University of Bristol
Jan 12, 2015
Siegel modular forms of degree 2: Fourier coefficients,
L-functions, and functoriality
Dr Dipramit Majumdar
IISER Pune
Jan 05, 2014
An introduction to Eigenvarieties
Prof Wintenberger Jean-Pierre University
of Strasbourg, France
Nov 06, 2014
Ramification and Iwasawa theory
IISER Pune
Nov 03, 2014
Hecke Theory for GL2 and converse theorem
IISER Pune
Oct 27, 2014
Tate's thesis and Hecke Theory for GL2
Dr Steven Spallone
IISER Pune
Oct 13, 2014
(g,K)-module
Speaker
Dr Supriya Pisolkar
IISER Pune
Oct 10, 2014
Jacquet Functors
Dr Baskar Balasubramanyam
IISER Pune
Sept 15, 2014
Principal series representations, parabolic induction
IISER Pune
Sept 08, 2014
Whittaker Functionals
IISER Pune
Aug 25, 2014
Global representations of GL(2)
IISER Pune
Aug 20, 2014
Representations of GL(2) over non-archimedean places
Dr Steven Spallone
IISER Pune
Aug 11, 2014
Representations of GL(2) over archimedean places
Dr Ronnie Sebastian
IISER Pune
Aug 04, 2014
Automorphic forms as function of adele groups
Dr Supriya Pisolkar
IISER Pune
May 21, 2014
Witt vectors and Hasselholt's Conjecture
IISER Pune
Apr 30, 2014
Overconvergent modular symbols
IISER Pune
Apr 23, 2014
Exceptional zero conjecture
IISER Pune
Apr 16, 2014
Two variable p-adic L-functions
IISER Pune
Mar 26, 2014
Explicit construction of the p-adic distribution attached
ordinary elliptic Hecke eigenform
IISER Pune
Mar 19, 2014
p-adic L-functions attached to modular forms
IISER Pune
Mar 12, 2014
Siegel modular forms and automorphic representations
Date
Title of the Talk
Dr Xavier Viennot
Emeritus research director at CNRS
Feb 17, 2015
Trees in various sciences
Dr Shilpa Gondhali
University of Haifa
Feb 03, 2015
Higher Toda brackets and Massey products
Dr Umesh Dubey
IISc, Bangalore
Jan 30, 2015
Twisted sheaves and twisted integral transforms
Dr Florian Sprung
Princeton University
Jan 15, 2015
Rational points of modular abelian varieties in towers of
number fields: How to bound the rank
Dr Nikhil Savale
Lumpkins Visiting Assistant Professor,
University of Notre Dame
Jan 07, 2015
Asymptotics of the eta invariant
Visitors’ Seminars
Speaker
Dr Swarnava Mukhopadhyay
University of Maryland
Jan 06, 2015
Rank-Level duality and Conformal Blocks divisors
Dr Shibasish Dasgupta
Department of Information Systems and
Analytics - Miami University, Ohio
Jan 02, 2015
A Bayesian Predictive Approach to Design Studies for
Comparing Biomarkers
Dr Pritam Rajan
Acadia University, Canada
Dec 23, 2014
Sequential design schemes for efficient estimation of
pre-specified process features in computer experiments
Prof Siegfried Boecherer
Institut für Mathematik - Universität
Mannheim, Germany
Oct 29, 2014
Congruence primes for Siegel modular forms via
twisted L-functions.
Dr R Venkatesh
TIFR, Mumbai
Oct 24, 2014
Unique Factorization of Tensor Products for finite
dimensional simple Lie Algebras
Dr Arnab Mitra
Ben-Gurion University of the Negev
Sept 26, 2014
Norm correspondence for unipotent radicals in classical
groups
Dr Anandam Bannerjee
TIFR, Mumbai
Aug 28, 2014
Tensor Structure on Smooth Motives
Dr Anandam Bannerjee
TIFR, Mumbai
Aug 26, 2014
Equivalence relations on algebraic cobordism
Dr Manoj Gopalkrishnan
TIFR, Mumbai
Aug 12, 2014
The Geometry of Reaction Networks
Prof Jeffrey Adler
American University
Jul 30, 2014
Lifting representations of finite reductive groups
Dr Asilata Bapat
University of Chicago
Jul 23, 2014
Morse theory and intersection cohomology
Prof Steven Weintraub
Lehigh University
Jul 09, 2014
A generalization of continued fractions
Prof R Parthasarathy
Bharathiar University, Coimbatore
May 22, 2014
On the modules $A_{(\mathfrak q, \lambda)}$
Dr Krishna Kaipa
IISER Bhopal
Apr 22, 2014
Linear Codes and Grassmannians
Dr Kashyap Rajeevsarathy
IISER Bhopal
Apr 07, 2014
Multicurves and primitivity in Mod(Sg)
Date
Title of the Talk
Prof Siddhartha Bhattacharya
TIFR, Mumbai
Nov 10-14,
2014
A brief introduction to ergodic theory (Mini course)
Prof Jose Ignacio Burgos Gil
ICMAT, Madrid Spain
Nov 04-07,
2014
Arakelov geometry of toric varieties (series of 4
lectures)
Prof Ramanan
CMI, Chennai
Mar 18 - Apr
01, 2014
Mini-course on Algebraic Geometry
Dr Stefan Friedl
University of Regensburg
Mar 05 - 12,
2014
The geometrization theorem for 3-manifolds (series of 3
lectures)
Mini-courses by Visitors
Speaker
Minor Thesis Seminars
Speaker
Date
Title of the Talk
Jul 11, 2014
Computing Hodge-Deligne Numbers of Hypersurfaces
on Toric Varieties
Mr Sudhir Pujahari
Jul 2, 2014
Graph Homomorphisms
Mr Prabhat Kumar Kushwaha
Apr 24, 2014
Ito Calculus Without Probabilities
Ms Manidipa Pal
Apr 14, 2014
Can one hear the shape of a drum?
Mr Pralhad Shinde
Mar 23, 2014
Extremal first Dirichlet Eigenvalue for the Laplacian and
Dihedral Symmetry
Mr Makarand Sarnobat
Mar 12, 2014
A topological Proof of Grushko's Theorem
Ms Gunja Sachdeva
Mar 10, 2014
Membership Problem in the Bitprobe Model
Date
Title of the Talk
Mar 12, 2015
The Local Langlands Correspondence
Ms Neha Prabhu
Mar 5, 2015
Quadratic Reciprocity: A proof using Algebraic Number
Theory-Part 2
Ms Neha Prabhu
Feb 26, 2015
Quadratic Reciprocity: A proof using Algebraic Number
Theory-Part 1
Mr Prabhat Kushwaha
Feb 12, 2015
What is Public Key Cryptography and why do we need
it?
Mr Sushil Bhunia
Jan 29, 2015
Clifford Algebras and Spin Groups
Ms Manidipa Pal
Nov 19, 2014
Siegel modular forms
Ms Manidipa Pal
Nov 12, 2014
Siegel modular forms
Ms Neha Prabhu
Nov 5, 2014
Introduction to Classical Modular Forms
Ms Neha Prabhu
Oct 22, 2014
Introduction to Classical Modular Forms
Oct 22, 2014
Representation Theory of Finite groups
Mr Hitesh Raundal
Student Seminars
Speaker
Oct 8, 2014
Ms Ayesha Fatima
Sept 24, 2014
Ms Ayesha Fatima
Sept 17, 2014
Symposia, Conferences & Events
Symposium on Math-Finance
March 5, 2015
Organizer
Anindya Goswami
This half-day in-house symposium on Math-Finance was organized to
give the students an overall knowledge of research works in Math-finance
being done in the department. This was open to all from IISER Pune and
required no prior registration.
There were three sessions
with two short breaks. The
sessions were chaired by Dr
Anup Biswas, Prof Uttara
Naik-Nimbalkar
and
Dr
Anindya
Goswami
respectively. Four students
(Sanket Nandan, Shirish
Kulhari, Nimit Rana and
Akash Krishna) presented
their Master’s project work.
This
was
the
first
symposium organized by the department where students had an
opportunity to present their ongoing research. The talks in the symposium
were on advanced research topics; nevertheless, efforts were made to
make basic ideas tangible. In particular, the mathematical formulation of a
real world problem, the relevant mathematical and statistical techniques
were clarified carefully. A good number of students from inside and
outside IISER Pune attended the event.
Home page:
https://sites.google.com/site/anindyagoswami/home/symp2015
ICTS Program on Advances in Mathematical Biology
December 7-16, 2014
Organizers
LS Shashidhara, Pranay Goel and Sujatha Ramdorai
In addition to ICTS and IISER Pune, this Program was also supported by
the Pacific Institutes of Mathematical Sciences (PIMS), Canada. The
Program brought together leading mathematical biology researchers from
Canada together with Indian scientists to deliver a series of pedagogical
lectures on contemporary topics of interest. The opening lectures by
Pranay Goel on the first day were an introduction to some essential
mathematical techniques that were useful to later topics. The rest of the
time was divided between three themes:
1. Mark Lewis, Daniel Coombs and Pauline van den Driessche lectured
on topics in Ecology, Epidemiology and Immunology. Milind Watve, Ram
Rup Sarkar and Sutirth Dey participated in the Discussions sessions
centred on these topics.
2. Subhash Lele, Anil Gore, Shailaja Deshmukh and Akanksha Kashikar
delivered lectures on Statistical inference in biological systems.
3. Lectures on Collective behaviour in cellular and organismal biology
were delivered by Sitabhra Sinha, Debashish Chowdhury, Somdatta
Sinha and Madan Rao. Collins Assisi participated in the discussion
session on the topic.
Over 65 participants attended the Program from both Pune and all over
India. The participants were drawn from varied backgrounds, rooted in
theoretical science in some form or another, be it physics or mathematical
biology or bioinformatics and so on. The participants were mostly at the
early PhD level although some faculty and younger students also
attended.
The atmosphere was vibrant with a very active participation from
students, which was well appreciated by the speakers. The participants
as well as speakers gave excellent feedback. All seemed to welcome the
breadth of lectures, the high quality of the Program, the organization
itself, and were generally pleased to have participated in the meeting.
The Program’s success indicates just how attractive topics in
mathematical biology are for students in the country at this time. It speaks
to a burgeoning development of the field, and the awareness and maturity
of the participants begs for an even greater investment in the conduction
of such Programs that will disseminate high quality instruction to a very
willing audience.
Mathematics Research Advisory Council
July 26-28, 2014
The MRAC consists of the following five mathematicians of eminence:
Professor Manindra Agarwal, Indian Institute of Technology, Kanpur
Professor TR Ramadas, Chennai Mathematical Institute
Professor Ram Murty, Queen's University, Kingston, Canada
Professor Dinesh Thakur, University of Rochester, USA
Professor SRS Varadhan, Courant Institute, New York, USA
The first four members visited IISER Pune campus from July 26-28, 2014.
The campus visit started with the Coordinator of Mathematics giving a
presentation on mathematics at IISER Pune. This was followed for the
next three days with meetings with each individual faculty member lasting
for about 30 minutes; a meeting with each of the two postdocs; a meeting
with all the mathematics PhD students; and a meeting with BS-MS
students including the 5th year project students. At the end of their
campus visit, the MRAC met with all discipline Coordinators and the
Director to give their feedback about the entire mathematics programme.
Later, they sent in their feedback in writing with critical comments and
recommendations.
"Overall, the mathematics department is doing very well and is on track for becoming a
leading department in India in terms of both teaching and research. Its present research
strengths include number theory, representation theory and algebraic geometry. These
areas are not unrelated to some of the other research areas of the department such as
coding theory, graph theory, algebra and analysis and so there is room for some
collaborative seminars amongst some of the research groups. In addition, the fact that
IISER Pune has been the venue for high level research conferences and workshops, is
an indication that it is moving in the right direction. The idea for PhD students to do a
minor thesis before they embark on their doctoral thesis enables students to have a
broader view of mathematics. This is an excellent initiative that we have not seen at
many other universities. Clearly, some new and strategic appointments are needed to
buttress the existing strengths of the department. The mathematics department of IISER
Pune has had substantial growth and now has an impressive group of young faculty. It
is doing quite well under a very good leadership. It is already on the international map,
at least in the area of number theory and representation theory, because of the wellchosen high level research conferences and workshops organized or hosted here, as
well as the innovative outreach activities. It will be a leading mathematics department in
India once the other mathematics areas are also strengthened."
Young Women and Mathematics
July 25-27, 2014
Scientific Committee & Organizers
Anisa Chorwadwala (Convener);
Anita Naolekar; Jaya Iyer (Chair);
Mousumi Mandal; Pooja Singla
Thakur
The Symposium Young Women
and Mathematics (YWM-2014) was a follow-up of the Indian Women and
Mathematics (IWM) symposia held twice in the past. The first one was
IWM-2012 held at Institute of Mathematical Sciences, Chennai during
January 8-10, 2012 and the next was IWM-2013 held at IISER Pune
during July 26-28, 2013. The earlier IWMs were modeled to facilitate
interaction between women mathematicians who are established
researchers, and college teachers, and for undergraduate and graduate
students.
Keeping in mind the increasing number of young women researchers in
India in the recent years, the current meet, the third in the series, was
named as "Young Women and Mathematics (YWM) Symposium". With
National Board for Higher Mathematics (NBHM) India offering support for
this venture, over 70 young women mathematicians from all over the
country participated in the symposium. There were a few participants who
were of Indian origin, either working or pursuing their doctoral studies
abroad.
The plan of the symposium was to have (i) a few mini-courses, in order to
introduce advanced areas of mathematics, (ii) some plenary talks by
prominent researchers and (iii) some contributory talks by participants
from varied fields of mathematics. There were two mini courses, one on
“Knots, Graphs and Applications” and the second one was on "Lie
Algebras and Representations". There were 9 plenary talks delivered by
young women researchers from reputed Indian Institutes and Universities.
The range of subjects varied from Number Theory to Commutative
algebra, and from Homotopy Theory to Partial Differential Equations and
Harmonic Analysis. All these focused and motivational talks were
received with great enthusiasm from an informed audience.
There were around 15 contributory talks by researchers and post doctoral
students. These talks were held in three parallel sessions namely (1)
Analysis, (2) Algebra and its Applications and (3) Miscellaneous. There
was a talk on the impact of some results from algebraic geometry to
arithmetic circuits. The contributory talk by Seemin Rubab, NIT Srinagar
titled "STEM Career and Women: Situation in Kashmir Valley” was
interesting.
There was an invited talk by Dr Neena Gupta (INSA Young Scientist
Award Recipient this year) from ISI Kolkata on her celebrated work "On
Zariski's Cancellation Problem". We also heard about her inspiring
journey (she being a young woman achiever).
There was also a poster presentation session by participants, which
showcased some interesting areas in mathematics. There was also a
panel discussion on a career in Mathematics in India in the current
scenario. The discussion focused on the funds and opportunities
available to women, present research/job opportunities in India etc. The
young audience comprising of graduate/ undergraduate students
benefited highly from this discussion.
The symposium concluded with a session on feedback from the
participants. In this age of specialization, many voices aired requests for
Group Discussions, to initiate collaboration among women working in
related areas. There was a very good suggestion that under the IWM
funding, a group of women mathematicians planning to have a
collaborative research work should gather at some specific location for a
reasonably sufficient period of time. They need not hold formal lectures
during this meet. They should hold discussions leading to the proposed
collaborative research work. Some participants also expressed that more
women of Indian origin, pursuing a career abroad should be invited to
share their expertise.
The Mathematics discipline of IISER Pune, its Coordinator Professor
Raghuram and Professor KN Ganesh, the Director of IISER Pune gave
their whole-hearted support to host the event.
Home page: https://sites.google.com/site/ywmiisc/home
Topology and Geometry of Surfaces Symposium
at the 29th Annual Conference of Ramanujan Mathematical Society
June 30-July 7, 2014
Symposium Organizers
Ravi Kulkarni, Tejas Kalelkar
Local Organizers
A Raghuram (Convener), Anisa Chorwadwala, Chandrasheel Bhagwat,
Kaneenika Sinha and SA Katre (Co-convener)
Invited Speakers
Moira Chas (Stonybrook University), Ara Basmajian (CUNY)
This symposium was part of the 29th Annual Conference of the
Ramanujan Mathematical Society held in the week after the conclusion of
the main events. It consisted of a mini-course on ”Computer driven
theorems and questions in geometry”
by Prof Moira Chas and a mini-course
on ”Identities of Hyperbolic surfaces” by
Prof Ara Basmajian. Apart from
students of IISER Pune, we also had
participants from IISER Mohali, Pune
University, Fergusson College and from
industry.
Homepage
29ac.ramanujanmathsociety.org
The 29th Annual Conference of Ramanujan Mathematical Society
June 23-27, 2014
Local Organizers
A Raghuram (Convener), Anisa Chorwadwala, Chandrasheel Bhagwat
Kaneenika Sinha, and SA Katre (Co-convener)
Invited Speakers
Hyman Bass, V Suresh, KB Athreya, S Weintraub, Dinesh Thakur, G
Rangarajan, S Sane, K Shiohama, S Thangavelu and Amiya Mukherjee
The RMS meeting is an annual event
organised by RMS to promote
mathematical research in India. With
an attendance of more than 300
people, including junior and senior
researchers from a wide range of
institutions and universities across
India, this is possibly the biggest
annual mathematical event in India.
We were extremely delighted to host
this important event at IISER Pune in
2014.
Apart from plenary talks by highly
accomplished
researchers
and
educators from across the world like
Hyman Bass (University of Michigan,
USA), Amiya Mukherjee (ISI Kolkata),
KB Athreya (Iowa State University,
USA), Dinesh Thakur (University of
Rochester, USA) and K Shiohama
(Fukuoka University, Japan), Weintraub (Lehigh University, USA), SS
Sane (IIT Bombay), G Rangarajan (IISc, Bangalore) and S Thangavelu
(IISc, Bangalore), there were parallel symposia in several exciting
research areas like Number Theory, Partial Differential Equations,
Harmonic Analysis, Riemannian and Finsler Geometry, Complex Function
Theory, Finite Groups, Logic, Discrete Mathematics, Topology and
Geometry of Surfaces.
An entire day was devoted to talks by experts on many recent advances
in Mathematics which originate from Ramanujan's work. There were also
several opportunities for graduate students to present their research work
to a wide audience during contributed talk sessions.
This meeting is very special because we hosted it at our Lecture Hall
Complex almost immediately after it was dedicated to the nation by the
President of India. We were able to accommodate almost all the
participants in our brand new hostel and guest house buildings.
Organizing an event of this magnitude and hosting huge number of
participants at a new institute like ours was a huge administrative
challenge. This was accomplished seamlessly through coordination
between the Mathematics group, technical team, finance section, hostel
and guest house staff, canteen staff and transport managers. Participants
from all over the world and RMS executive committee members were
highly impressed with the academic facilities and technical equipment
made available by the institute. In fact, thanks to the near perfect
execution of this meeting, RMS formally requested IISER Pune to host a
joint meeting of RMS and Indian Mathematical Society with the American
Mathematical Society --an international event of far bigger proportions in
2016!
Homepage 29ac.ramanujanmathsociety.org
Number Theory Symposium
at the 29th Annual Conference of Ramanujan Mathematical Society
June 23-27, 2014
Symposium Organizer
Debargha Banerjee
Local Organizers
A Raghuram (Convener), Anisa Chorwadwala, Chandrasheel Bhagwat,
Kaneenika Sinha and SA Katre (Co-convener)
Invited Speakers
M Manickam (KSOM), VG Narasimha Kumar (IIT, H), Supriya Pisolkar
(IISER Pune), Baskar Balasubramanyam (IISER Pune), B. Ramakrishnan
(HRI), K Srinivas (IMSC), S Katre (UoP).
The number theory symposium started this year as part of the annual
Ramanujan Mathematical Society meeting. This conference was
supported by NBHM.
Homepage 29ac.ramanujanmathsociety.org
ICTS Program on p-adic Aspects of Modular Forms
June 10-20, 2014
Organizers
A Raghuram, Baskar Balasubramanyam, Haruzo Hida, Jacques Tilouine
Invited Speakers
(a) For the workshop: R. Sujatha, Jacques Tilouine, Baskar
Balasubramanyam, David Geraghty, Mladen Dimitrov, Haruzo Hida, A.
Raghuram and Debargha Banerjee
(b) For the advanced discussion meeting: Jeanine van Order, Haruzo
Hida, Baskar Balasubramanyam, Olivier Fouquet, Chandrakant Sharma,
Giovanni Rosso, Riccardo Brasca, Denis Benois, Mahesh Kakde, David
Geraghty, Ming-Lun Hsieh, Devika Sharma, Fabian Januszewski, Eknath
Ghate, Tadashi Ochiai, Mladen Dimitrov, Sudhanshu Shekhar, Ashay
Burungale, Jacques Tilouine
The aim of this program was to focus on the p-adic aspects of modular
forms and related topics. The program consisted of two components, an
instructional workshop followed by a discussion meeting. There were
seven mini-courses in the workshop that focused on two broad themes:
on p-adic families of automorphic forms with some modularity lifting
applications in mind and on the construction of p-adic L-functions in
various situations and their applications.
The final part of the program was a three day discussion meeting in which
the state of current research in these topics were discussed.
Homepage http://www.icts.res.in/program/PAMF2014
Pune-Mumbai Number Theory Seminar
April 4-5, 2014
Organizers
Debargha Banerjee, Eknath Ghate, Ravi Raghunathan,
Invited Speakers
Jyoti Sengupta (TIFR), Amiya Kumar Mondal (IIT,B), Debargha Banerjee
(IISER,P), Steven Spallone (IISER,P), Ravi Raghunathan (IIT,H), CS
Rajan (TIFR)
The inaugural Pune-Mumbai number theory
meeting was organized at the Department
of Mathematics, IIT Bombay. The aim of
this seminar was to increase collaboration
and interaction among the number theorists
at IISER Pune, IITB and TIFR. This event
has provided an opportunity for young
number theorists to interact and collaborate
with established mathematicians and is
planned to be organized regularly every
year/semester.
Homepage
https://sites.google.com/site/punebombaynumbertheoryseminar/
Mathematics Day 2014
March 08
The 2014 Math day had several following fun events along with a colloquium by Prof MS
Narasimhan.
• We tested our mental arithmetic with the Shakuntala Devi Competition!
• Players squared off against an opponent in the Room of Games, in which you'll clash over
NIM and Hackenbush, and learn the math to step up your game.
• We returned to LHC 101 for three party-type math games in the "Math Carnival".
• There were two activities in the Room of Symmetries: For one, we learned to make,
decorate, and manipulate our own Hexaflexagons. We also learned the secrets of the
timeless 15 Puzzle of sliding tiles, and its exotic variations!
• At the "Bubbles as Minimal Surfaces" workshop, we formed manifold shape-optimizing
surfaces with soap and wires.
• The Prime Number Bee began at noon, which proceeded as follows: Students lined up as in
a spelling bee, and successive students recited the prime numbers 2,3,5, ... Any student who
gave a composite number, skipped a prime, or took too long had to sit, and the last two
standing received a cash prize. Chandrasheel taught us some prime number trivia along the
way.
• Women in Math Poster Competition and Showcase was conducted by Anisa during which
teams of students designed a poster and quick talks to compete for a cash prize. Afterwards
we watched the beloved Math Day Skit, bringing Scotland Yard to Pune with the "Sherlock
Holmes: Game of Chances"!
• Then we had our eminent guest MS Narasimhan deliver his lecture "Mathematical Research
in India after Independence: The Early Years", followed by the Award Ceremony where we
celebrated our winners.
• Hard-core mathletes returned at 11pm for the CRYPTEX finals: our "Mathematical Treasure
Hunt".
A Glimpse of Life in Math@IISER Pune
At work…
With Mathematics Research Advisory
Council (MRAC) Members
Turning coffee into theorems…
At Amlan’s
farewell party
WAY
The
Rationality
is
Overrated
Indian Institute of Science Education and Research (IISER) Pune
Dr Homi J Bhabha Road, Pashan, Pune – 411 008, Maharashtra, India
Phone: +91 20 2590 8001 Fax: +91 20 2586 5086
Website: www.iiserpune.ac.in

Profile book 2015

Transcription

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