Brochure - Centre de recherches mathématiques

Pure and
fundamental
The largest
research
centre
in Québec
The Centre
de recherches mathématiques
(crm) is the
largest research centre in Québec and one of the most
important mathematics research centres in the world.
The crm was created in 1968 at the Université de
Montréal and gathers all the stakeholders in mathematical
research at Québec universities and some other Canadian
universities. The crm organizes events attended by
researchers from all over the globe and representing
all mathematical disciplines. The crm focuses on pure
and applied mathematics in all areas of human activity,
for instance theoretical physics, brain and molecular
imaging, quantum information, statistics, and genomics.
Indeed mathematics is both the first science and the
servant of experimental science, which draws upon its
new concepts, its language, and its methods.
Fonds de recherche
sur la nature
et les technologies
1
A bird eye’s view of the CRM Thematic Program
Each semester the CRM chooses
The CRM members belong a topic at the forefront of
mathematical research (in pure or
to ten laboratories applied mathematics) and organizes
corresponding to specific
mathematical disciplines
workshops and lectures on this topic.
Aisenstadt Chairs
World-renowned mathematicians
and including researchers are invited to give the Aisenstadt
Chair lectures, which are usually
from several universities. related to the thematic program
The CRM has many diverse programs;
here is an overview of these programs.
of the current semester.
General Program
The CRM organizes and supports
financially workshops and
conferences in all fields of
mathematics.
A centre
with many
programs
ateurs
Organizers/Organis
(Montréal)
Octav Cornea
(Tel Aviv)
ich
erov
Polt
Leonid
(Bruxelles)
Felix Schlenk
2
Participants
olo (Pisa)
Alberto Abbondand
(New York)
Peter Albers
(MIT)
Denis Auroux
(Tel Aviv)
Paul Biran
(Bruxelles)
is
rgeo
Frédéric Bou
(Montréal)
Ozgur Ceyhan
(Moscow)
v
kano
Yuri Che
(Haifa)
Misha Entov
(München)
lder
enfe
Urs Frau
(Kyoto)
Kenji Fukaya
(Santa Cruz)
burg
Ginz
or
Vikt
(Montréal)
Basak Gürel
(Bruxelles)
Muriel Heistercamp
(Notre Dame)
Richard Hind
(New York)
Helmut Hofer
(Montréal)
Hu
Shengda
(Toronto)
Yael Karshon
Ely Kerman
François Lalonde
Janko Latschev
Samuel Lisi
Guangcun Lu
Klaus Mohnke
Alex Oancea
Kaoru Ono
Yaron Ostrover
Dietmar Salamon
Matthias Schwarz
Ivan Smith
Claude Viterbo
Katrin Wehrheim
Kris Wysocki
Edi Zehnder
Fabian Ziltener
Multidisciplinary
and industrial program
Champaign)
(Urbana
(Montréal)
(Zürich)
(Stanford)
(Nankai)
(Berlin)
(Strasbourg)
(Sapporo)
(MIT)
(Zürich)
(Leipzig)
(Cambridge)
(Palaiseau)
(MIT)
(Penn State)
(Zürich)
(Toronto)
Mathematics are used in all of the
sciences and the CRM organizes or
supports numerous activities related to non-mathematical sciences
and problems arising in industrial,
governmental, or medical settings.
Industrial Problem
Solving Workshops
Every two years the CRM organizes
an Industrial Problem Solving
Workshop in order to help solve
problems brought forth by
companies or public or non-profit
organizations.
SMS Summer School
This summer school goes back to
1962 and was financed by NATO
over a long period of time. Initially it
was organized by the Deparment of
Mathematics and Statistics of the
Université de Montréal but it is now
organized jointly by that department
and the CRM. It is one of the oldest
and most important scientific
schools in the world.
.
Prizes
The CRM awards prizes either on
its own or in collaboration with
other mathematical institutes and
professional associations such as
the Statistical Society of Canada
and the Canadian Association of
Physicists. In particular the CRM,
the Fields Institute, and PIMS jointly
award the most important Canadian
mathematical prize.
Postdoctoral Scholarships
The “Grandes conférences
The CRM runs a prestigious program du CRM”
of postdoctoral fellowships in collaboration with the Institut des sciences
mathématiques (ISM). This program
enables young researchers from all
over the world to come to the CRM
and work with CRM members.
The Grandes Conférences du CRM
are lectures geared towards a
broad audience and allow the CRM
to present to the public the latest
advances in mathematics. One goal
of these lectures is to develop the
scientific culture of the community.
Publications
The CRM is responsible for some
collections published by Springer
and the American Mathematical
Society. It also publishes monographs, proceedings, lecture notes,
software, and videos.
Colloquia
The CRM organizes the
CRM-ISM Mathematics
Colloquium and the
CRM-ISM-GERAD Statistics
Colloquium. These are weekly
colloquia and feature worldrenowned mathematicians and
statisticians who come to Montréal
to present their most recent work.
Mathematics
of Planet Earth 2013
The CRM has proposed a wideranging program on the Mathematics
of Planet Earth, which has been
embraced by the most prestigious
mathematics institutes in the world.
3
The CRM thematic Each year or each semester, the CRM Fields medal, the equivalent of the
Nobel Prize for mathematics).
program organizes activities related to a
Each year or each semester,
topic at the leading edge of the
mathematical sciences.
These activities include workshops,
the CRM organizes Aisenstadt Chair lectures, and summer
schools. They attract hundreds of
activities related to mathematicians from all over the
world and postdoctoral fellowships
a topic at the leading edge are offered to young researchers
in order to foster collaborations
of the mathematical sciences. between them and the CRM
members. Here are some instances
of recent thematic programs.
In 2008-2009 the CRM organized
a thematic year on probabilistic
methods in mathematical physics.
The program included 10 workshops and three series of lectures
by Aisenstadt Chairholders (among
whom two had been awarded the
Many CRM activities pertain to
applications of mathematics. The
Fall 2009 semester was devoted to
medical imaging (used by medical
investigators) and quantum imaging
(used by researchers in chemistry).
The topics of the first and second
semesters of 2010 were respectively number theory and group
theory, two branches of pure
mathematics that now have many
applications in cryptography and
theoretical computer science.
The Winter 2011 semester was
devoted to statistics and consisted
of 7 workshops, in particular workshops on meteorology, genomics,
and health research.
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ATELIERS
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An abundance of new ideas
5
The CRM laboratories The members of the CRM
Analysis Laboratory specialize
in a field that is both classical
As well as organizing many and at the centre of modern
mathematics.
activities that are international
in scope, the CRM brings structure to The members of CICMA
(Interuniversity Centre in Algebraic
the research carried out by Computation) specialize in algebraic
© from the web site of David Xianfeng Gu
number theory, analytic number
Québec mathematicians. theory, group theory, and
moonshine.
Almost all Québec researchers
The members of CIRGET
in mathematics belong (Interuniversity Research Centre
in Geometry and Topology) are
to at least one CRM laboratory. experts in differential geometry,
topology, algebraic geometry, and
geometric group theory.
Researchers
working in all areas
of mathematics
6
The GIREF (Interdisciplinary
Research Group in Finite Element
Methods) is based at Université
Laval in Québec City and its
researchers specialize in numerical
modelling and simulation and
numerical methods, in particular
for solving industrial problems.
The INTRIQ (Interdisciplinary
Institute for Quantum Computing)
is an association of researchers who
use quantum mechanics in order to
solve in novel ways problems arising
in computer science and information theory.
The LaCIM (Laboratory of
Combinatorics and Mathematical
Informatics) was created in 1982
and is based at UQÀM. Its members
specialize in enumerative combinatorics, algebraic combinatorics,
bioinformatics, and mathematical
aspects of computer science.
The Applied Mathematics
Laboratory gathers researchers
interested in applications of
mathematics (to mechanics of
fluids and solids, physics, biology,
etc.). Its members use a broad
variety of tools, especially tools
from optimization, numerical
analysis, and dynamical systems.
Ever since the CRM was founded,
the Mathematical Physics group
has been one of its strongest
research associations. The mathematicians in the Mathematical
Physics Laboratory conduct
research in the most up-to-date
areas of their field (especially
classical and quantum integrable
systems, random matrices, conformal
field theory, percolation, the spectral
theory of Schrödinger operators,
and the study of symmetry in
difference equations).
haemodynamics responses in
optical imaging, inverse problems
and wavelets, seizure prediction
for epileptic patients with implants,
metrics to evaluate the clinical
impact of variable drug intake
behaviour, and pharmacometrics.
The CRM Statistics Laboratory
gathers statisticians who are leaders
in their respective research areas
and work in such branches of statistics as statistical learning and neural
networks, survey methodology,
functional data analysis, statistical
The PhysNum Laboratory (where image analysis, dependence struc“PhysNum” stands for “Numerical
tures, Bayesian analysis, time series
Physics”) gathers researchers
and financial data analysis, and
working in medical imaging and
resampling methods.
pharmacokinetics. Among specific
research topics let us mention
cerebral activation networks,
analysis • algebra • number theory • geometry • topology •
numerical methods • quantum informatics • combinatorics
applied mathematics • imaging • statistics • mathematical physics
7
The CRM Multidisciplinary One of these researchers is
and Industrial Program André Bandrauk, who holds
Among members of the CRM
one finds researchers
from other disciplines
who use mathematics
and appreciate its
contribution to
other research fields.
the Canada Research Chair in
Computational Chemistry and
Molecular Photonics at the
Université de Sherbrooke. He
has just been named an Officer
of the Order of Canada.
Yoshua Bengio and Gilles
Brassard, both professors at the
Université de Montréal, are the
respective holders of the Canada
Research Chair in Statistical
Learning and the Canada Research
Chair in Quantum Informatics. In
2009 Gilles Brassard received the
Gerhard Herzberg Canada Gold
Medal for Science and Engineering
(the highest NSERC award).
Since 2007 the CRM has been
organizing Industrial Problem
Solving Workshops. Companies
or other institutions are invited
to submit problems that are then
modelled, studied, or completely
solved by teams consisting of
Montréal professors, experts from
other cities or countries, and students.
These workshops are “incubators”
of collaborations between universities
and enterprises.
Relations with
Other Fields
8
«
For Solving Problems
testimony
The August 2011 Industrial Problem Workshop enabled us to
present a framework for estimating the wind resource of an Aeolian
Farm to a team consisting of university researchers and students
from three universities. Collectively the team members had expertise
in statistics, mathematics, and physics. They examined the current
methodology in detail and proposed new and original solutions for
this concrete engineering problem (a very important one within our
industry). The week unfolded in a very friendly atmosphere and the
team work was productive and successful. Also we had a great
opportunity to learn about and discuss the problems examined
by the other teams.
»
We are grateful to the CRM for having organized an Industrial
Problem Solving Workshop. We have much appreciated taking part
in the workshop and it has allowed knowledge to be exchanged
between industrial and academic representatives. In summary it was
a great experiment in industry-university collaboration.
Michel Carreau, Hatch
Hatch is a professional services firm that delivers a comprehensive
array of services to the Mining, Metallurgical, and Energy sectors.
«
In 2009 we were trying to design a method for optimizing
dynamic transfer limits in the Hydro-Québec/TransÉnergie high
tension network. The workshop allowed us, with the help of a
professor and some students, to build an abstract model of our
problem and find optimization methods for solving it. At the end
of the week a heuristic algorithm had been proposed and two of
the students were already working on its implementation. They were
interested in pursuing their work and gave us a prototype of the
software we needed. The solution implemented at TransÉnergie in
2010 grew directly out of this prototype and is now a basic tool for
the engineers who design the network exploitation strategies. The
workshop enabled us to make rapid progress and have stimulating
exchanges with academic researchers, in a relaxed atmosphere.
Our experience was as useful as it was pleasant. We are very happy
to have taken part in such a workshop.
André Bandrauk
»
Yoshua Bengio
testimony
Jean-Claude Rizzi and Guy Vanier
Electrical Networks and Mathematics
IREQ, Hydro-Québec Research Institute
Gilles Brassard
9
The SMS
Summer School
and Postdoctoral
Fellowships
The SMS school was created at
The SMS Summer School
(Séminaire de mathématiques the request of the Department of
Mathematics and Statistics of the
supérieures)
This summer school in pure and
applied mathematics has been held
for 50 years on the campus of the
Université de Montréal. Each SMS is
devoted to a topic at the forefront
of mathematical research and gathers lecturers of the highest calibre
and students from all over the
world. These students are mostly
graduate students completing
their studies. The summer school
consists of around 12 minicourses
(each of which lasting 5 hours).
Université de Montréal and was
originally financed by NATO. Since
2011 the school’s principal partner
is the CRM but it is also supported
by the other Canadian mathematical institutes (the Fields Institute
and the PIMS) and by the MSRI
(Berkeley, California).
Graduate training
and postdoctoral
fellowships
«
01
2
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June 21 – juillet 201
21 juin – 2
10
Organiz
Michael Rubing Committe
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Uppsala
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Speakers
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Andrew Boo
Henri Dar ker
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Noam Elki
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Dorian God
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Eyal Goren
Dennis A.
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McGill Univ ateurs locau
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McGill Univ
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Centre de
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Fields Inst
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Institut des
sciences
National
mathématiq
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Université nce Foundation
de Montréa
University
l
of Waterlo
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Application
Date limi deadline: March 15,
te pour les
candidature 2009
s : 15
mars 200
9
raf.ca
/ Organis
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: www.neog
Sponsor
graphique
Local Or
Henri Dar ganizers
mon
Eyal Goren
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d’organisa
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Committee ersité de Montréal
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Alain Tapp
Tel-Aviv Un itute for Theoretical
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Inst
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Julia Kem
Pe
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Daniel Got
Université
Rousseau
Christiane
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/ Conféren
Speakers
assachuset ontréal
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Scott Aaron
Université
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of Waterlo
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Gilles Bras
University
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Richard Cl
Pe
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Daniel Got
McGill Univ
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Physics an
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Patrick Ha
Tel-Aviv Un itute for Theoretical
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Julia
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Raymond
ETH Zuric
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Renato Re
University
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Paris Sud
Barry Sand
Université
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University
of
McGill Univ Bristol, UK
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Harvard Univ ty, Canada
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Columbia
Univ
McGill Univ ersity, USA
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Uppsala
University, ada
Kamal Khu
Swe
University
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Erez Lapid
American
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Univ
Michael Rub
Hebrew Univ ersity of Beirut,
Lebanon
Harold Star instein
University ersity of Jerusale
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of
Fredrik Strö
University Waterloo, Canada Israel
mberg
of
Andreas
Technische California at San
Strömbergss
Diego,
Universität
Audrey Terr
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Uppsala
Darmstadt, USA
as
University,
Akshay Ven
Germany
Swe
University
katesh
of Californ den
John Voig
Stanford
ia at San
ht
University,
Diego, USA
USA
University
of Vermont,
* to be con
USA
firmed/à
confirmer
Postdoctoral Fellowships
«
»
Stefan Friedl
University of Cologne
Graphic Des
tion
ign/Concep
graphique
: www.neog
raf.ca
testimony
The CRM-ISM Postdoctoral
Fellowships are very prestigious and
selective and they are awarded to
carefully chosen researchers. The
competition is open to promising
researchers from all parts of the
world who have obtained recently
(or are about to obtain) a doctorate
in mathematics. The fellowships are
awarded for two years and are
financed jointly by the CRM, the
ISM, and the CRM laboratories.
The CRM also finances up to 50%
of the cost of the postdoctoral
fellowships associated with
thematic semesters.
From 2006 to 2009 I was a CRM-ISM
postdoctoral researcher at the Centre
de recherches mathématiques.
These two years were the most productive
ones for my research. This was so
because I could devote myself entirely
to my research and also because many
professors, postdoctoral fellows,
and visitors were available for fruitful
exchanges. The unique Montréal
atmosphere and the friendly
environment provided by my
research group made my stay
in Montréal a very
pleasant one.
Antonio Lei
Miljan Brakocevic
My CRM postdoctoral fellowship
introduced me into the Montréal
“arithmetical” community and an
even larger community (thanks to
the 2005-2006 Thematic Year on
Analysis in Number Theory). The
contacts that started during the
Thematic Year are very important
for me and most of my current
projects and collaborations
originated during my time as
postdoctoral fellow.
»
Pierre Charollois
Université Pierre et Marie Curie
aterloo
ersity of W
Yasha Savelyev
11
testimony
«
10
010
The “Grandes
Conférences
du CRM”
While addressing varied topics
(cryptography, quantum information,
chaos in weather systems or financial
systems, brain imaging, and
biotechnology), these lectures all
Delivered by scientists renowned aim to reveal to a broad audience
the beauty and power of cuttingfor their communication skills, edge mathematical research. Here
are short descriptions of some of
the “Grandes Conférences du CRM” these lectures.
developments in the
mathematical sciences.
Cédric Villani
The flutter of a butterfly’s wings in
Brazil may trigger a snow storm in
Montréal. This statement captures
vividly the consequences of chaos
theory. Have mathematics lost their
predictive power? Étienne Ghys
(from the École Normale Supérieure
de Lyon) answered this question
by using concrete examples such
as the Lorenz Water Wheel and by
explaining the power of probabilistic
predictions. We were not surprised
when Le Devoir (a daily newspaper) devoted its front page to the
lecture by Étienne Ghys!
c
n
e
r
é
f
on
C
s
e
d
n
a
r
are geared towards a public eager
to understand the most striking
The butterfly effect
G
F
E
’
«L
L
I
P
A
P
FE T
Promoting
scientific
knowledge
The grandes conférences
12
The end of the solar system? The laws of disorder
A struggle between titans
Is a collision between two planets
possible? By recalling the efforts
made by scientists since Antiquity
to answer that question, Jacques
Laskar (from the Observatoire de
Paris) summed up our knowledge
about the stability of the solar
system. What may we conclude?
Yes, a collision between Mercury
and Venus seems possible. Fortunately the probability of such an
event (at least within our lifetime)
is very small. New simulations by
Jacques Laskar, carried out after
his lecture at the Université de
Montréal, have shown that the
Earth itself is not immune from
a collision with one of the internal
planets.
In the XIXth century two great
British scientists, Charles Darwin
and Lord Kelvin, computed the age
of the earth. Their conclusions,
however, were incompatible. At the
time British society followed this
debate with passion. The “Grande
Conférence” by Cédric Villani (who
received a Fields medal in 2010)
was a survey of attempts to
compute the age of the Earth,
a sweeping portrait starting with
the oldest documents (e.g.,
the Book of Genesis in the
Old Testament) and ending
with recent advances.
férences du CRM
Can mathematical rules describe
the disordered motion of molecules
jostling together or the percolation
of run off water through the soil?
The “Grande Conférence” by Yvan
Saint-Aubin (from the Université
de Montréal) addressed this topic
while following an (almost) unpredictable path going from the efforts
of Robert Brown (a biologist) to
recent advances rewarded by a
Fields medal (in 2006). The path
also included an excursion through
the paintings of Jackson Pollock.
L
es Grandes ConférenCes du Cr
that
swings:
Les Grandes Conférences du CRM
hind the golf
Arnold
University of Minnesota
mathematics
vement chaotique du Système
solaire Those
DÉSORDRE
ET BEAUTÉ
have momentum!
Conférencier: Jacques
Laskar Yvan Saint-Aubin (U. de Mon
Conférencier:
et les mathématiciens ont longtemps
ver que le mouvement du Système solaire
me le remarque Henri Poincaré, plusieurs
lité du Système solaire se sont succédées,
ment, le mouvement des planètes dans le
it considéré comme le modèle même de
sultats de ces dernières années montrent
mouvement des planètes est chaotique, et
sible de prédire son évolution au delà de
ées environ, ce qui est très court par rapds d’années d’existence de notre Système
plications de ce mouvement chaotique ?
ur l’évolution du Système solaire sur plunnées ?
Science often gives an edge to
top-notch athletes. Can mathematics
help golfers too? In his “Grande
Doug Arnold (from the
prestige: Conférence”
Jacques Les
Laskarmathématiques
est astro- des conférences
ont,de parmi
leurs buts
prin- surveyed
University
of
Minnesota)
plénière
à
la
conférence
nome à cipaux,
l’Institut de celui
Méca- de trouver les motifs communs
à
efforts
at
devising
mathematical
internationale de
physique
nique Céleste
et de Calcul
plusieurs
observations,
soit
de
la
nature,
soit
de
mathématique en 1994, et models of golf, including the golfer’s
des Ephémérides
(IMCCE)
structures
abstraites.
de Paris. Il s’est fait con- des conférences Shrödinger, motion, the impact of the golf club
the ball’s motion, and
et Gödel. on the
naître par
travaux sur Mutch, Bernoulli
Lesesmathématicien
qui découvre
deball,
nouveaux
Jacques utilisera
Laskar publiesouvent
ré- finallylethe
optimization
le chaosmotifs
dans le ou
système
structures
mot
beauté of the ball
des articles de surface.
solaire etpour
sur ledécrire
rôle de lalagulièrement
compréhension ainsi gagnée, car sa
Lune dans le climat de la vulgarisation scientifique,
réussite
s’apparente
dans Science esthétique. Ce
Terre. Il est membre de notammentà l’expérience
sentiment
est
particulièrement
l’Académie des Sciences et vie, Pour la Science, La singulier quand
l’objet
est le etc.
désordre.
Il a donné Le conférencier
depuis 2003.
Ses d’étude
travaux Recherche,
décrira
des
sujets
où
les
mathématiques
ont réussi
se sont mérité plusieurs de nombreuses conférences
seul le désordre était
grand public etlàa où
participé
prix, dontà letrouver
Prix G. de des
Pon- structures
técoulantvisible.
de l’Académie à des vidéos et émissions de
des Sciences en 1993, le radio et de télévision, dont
L’exposé
à toutes
et tous et ne
deuxaccessible
avec Radio-Canada
en
Prix IBM
Excellenceseenveut
requiert
aucune
spécifique des
1993 etconnaissance
2003.
calcul intensif,
la médaille
d’argentmathématiques.
du CNRS, ainsi que
Jeudi 9 octobre 2008 • 20 h 00
Pavillon Jean-Coutu, Université de Montréal,
2940 chemin Polytechnique, S1-151
13
Professeur depuis
département de mathé
de statistique de l’U. d
Vendredi 28 novembre 2008 (de 20 h 00 à 21
Accromath
and the CRM
Publications
Accromath is a semi-annual
magazine produced by the ISM
and the CRM. The magazine is
distributed free of charge in the
high schools and junior colleges of
Québec, as well as in foreign countries. It is mostly geared towards
students and teachers in those
Le paradoxe
institutions. On June 15, 2012,
Accromath was awarded the
des Dupont
Anatole Decerf Prize, a prize that
is given every two years by the
Société mathématique de France
and the Fondation de France to
reward exceptional works of popularization or mathematical pedagogy.
The panel members stressed the
high quality of Accromath, from both
the scientific and pedagogic points
of view. This event marked the first
time that the Anatole Decerf Prize
had been awarded to a team not
based in France.
Rubrique des
Volume 6 • Hive
r–Printemps 2011
Numéro spécial
Développement
durable
Changements climatiq
ues et
Nosarticles
• L’effet papillo
n
• Au-delà de l’ef
fet papillon
• De la météo
au climat
• Impact des gaz
à effet de serre
• Jožef Stefan
et Ludwig Boltzm
ann
• L’eau sous nos
pieds
• Aspects statist
iques
de la gestion for
estière
• Jean le Rond
d’Alembert
World-class
publications
and outreach to budding scientists
Here are a few of the prizes
awarded to Accromath.
BRONZE
2007
OR
2010
Prix
Anatole
Decerf
2012
BRONZE
2011
Les mathématiques
au
Prix spécial
de la ministre 2009
France Caron
Université de Montréal
théâtre
Science du calcul, art de raisonner ou
de convaincre, ensemble de concepts
pour aborder de nouveaux problèmes,
moteur dans la quête d’un nouvel idéal,
… Selon l’époque ou le contexte, on a pu
faire jouer l’un ou l’autre de ces rôles aux
mathématiques. Il n’est donc pas étonnant
que des auteurs dramatiques aient été sensibles à ces différentes visions ou utilisations
des mathématiques, dans ce qu’elles révèlent
’être humain.
sur la société et sur l’être
La leçon - Eugène Ionesco (1951))
10
OR
2012
DossierArt
2008
Vol. 7 • été – automne 2012
14
Les mathématiques, dont l’exercice paraît a priori plutôt
solitaire et économe de mots, peuvent-elles se conjuguer
avec le théâtre ? Nous en donnons trois exemples
qui illustrent autant de visions des mathématiques.
Pour bien des gens, les mathématiques évoquent d’abord et avant tout les souvenirs
qu’ils en ont gardés de leur fréquentation à
l’école. Et de ceux-là, on retient souvent les
premiers apprentissages en arithmétique ou
en algèbre.
Dans La leçon, l’auteur roumain Eugène
Ionesco, père du théâtre de l’absurde,
trace un portrait terrible de l’éducation et
de la nature humaine. Avec un professeur
âgé, d’abord bienveillant, qui se transforme
sous nos yeux en dictateur puis en tortionnaire et assassin, Ionesco nous renvoie, au
lendemain de la deuxième guerre mondiale,
toute l’insignifiance et la bêtise qu’il perçoit
chez l’homme.
Voulant établir un portrait général des
connaissances de sa jeune élève de dix-huit
ans qui se destine, selon le souhait de ses
parents, à un « doctorat total », le professeur
choisit de commencer avec l’arithmétique,
malgré la mise en garde de la bonne :
« Vous feriez mieux de ne pas commencer
par l’arithmétique avec Mademoiselle.
L’arithmétique ça fatigue, ça énerve. »
Alors qu’elle détient deux baccalauréats en sciences et en lettres,
mmence par
l’élève de La leçon commence
ofesseur en
impressionner le professeur
ction l’art
maniant à la perfection
d’additionner 1 au nombre
n cela
précédent. Voyant en
ition,
une maîtrise de l’addition,
ntera
le professeur déchantera
sfert
face au difficile transfert
à la soustraction, où
l’élève se contenteraa
de deviner alors quee
le professeur voudraitt
qu’elle raisonne. Il
essaiera alors de lui
ens
faire travailler le sens
mpadu nombre par la compas, mais
raison des grandeurs,
uestions
il se heurtera à des questions
ne fille,
plutôt fines de la jeune
mpêtrer
qui le feront s’empêtrer
dans ses explications..
9
r–Printemps 200
Volume 6 • Été–Automne 2011
Volume 4 • Hive
Mesurer
l’Univers
n
Geststio
ocks de
Un modèle statistique
des
poissons
Autresarticles
ri e es
Trois pesées
suffisent
• Les équations
éjugés
n’ont pas de pr
ns impo
io
ct
tru
ns
co
s
• De
mathémati
• Découverte
e
à la polyvalent
r
le
Eu
rd
ha
• Leon
Euler
• Des ponts d’
ire
à la grippe avia
Nosarticles
• Les sphères de Dandelin
• Adolphe Quételet
de thé
• Mathématiques de la tasse
• La carte du cerveau
• Aller en ligne droite
sur une planète qui tourne
Rubrique des
Mona Lisa
au photomaton
Les mathématiques au théâtre | France Caron • Université de Montréal
Le professeur
L’élève
Vous savez bien compter? Jusqu’à combien Euh ... trois ou quatre? Quel est le plus
savez-vous compter?
grand? Le plus grand de trois ou quatre?
Dans quel sens le plus grand?
L’élève
Cela n’est pas possible, Mademoiselle.
L’élève
Alors, mettons jusqu’à seize.
Le professeur
Le professeur
Il y a des nombres plus petits et d’autres
plus grands. Dans les nombres plus grands
il y a plus d’unités que dans les petits.
L’élève
... Que dans les petits nombres?
Le professeur
Cela suffit. Il faut savoir se limiter. Comptez
À moins que les petits aient des unités plus
donc, s’il vous plaît, je vous en prie.
petites. Si elles sont toutes petites, il se
peut qu’il y ait plus d’unités dans les petits
Un ..., deux ..., et puis après deux, il y a trois nombres que dans les grands ... s’il s’agit
... quatre ...
d’autres unités ...
L’élève
Le professeur
L’élève
Arrêtez-vous, Mademoiselle. Quel nombre Dans ce cas, les petits nombres peuvent être
est plus grand? Trois ou quatre?
plus grands que les grands nombres?
Vol. 7 • été – automne 2012
Je puis compter ... à l’infini.
Le professeur
Le professeur
Laissons cela. Ça nous mènerait beaucoup
trop loin: sachez seulement qu’il n’y
a pas que des nombres ... il y a aussi
des grandeurs, des sommes, il y a des
groupes, il y a des tas, des tas de choses
telles que les prunes, les wagons, les oies,
les pépins, etc. Supposons simplement, pour
faciliter notre travail, que nous n’avons que
des nombres égaux, les plus grands seront
ceux qui auront le plus d’unités égales.
L’élève
Celui qui en aura le plus sera le plus grand?
Ah, je comprends, Monsieur, vous identifiez
la qualité à la quantité.
Cherchant apparemment à la voir employer
les raisonnements arithmétiques qu’il attend
d’elle, il multipliera les contextes qui ne
feront que gagner en absurdité (il prétendra
lui « ajouter » et lui « enlever » des oreilles
et des doigts), révéler ses pulsions intérieures
et éloigner sa pauvre élève des apprentissages visés.
La jeune fille connaîtra un court moment de
grâce lorsqu’elle répondra rapidement à la
demande de : « calculer mentalement combien
font, et ceci est la moindre des choses pour
un ingénieur moyen, combien font, par
11
The American Mathematical Society
(AMS) has been publishing and
distributing two collections of the
CRM since 1992, namely the
CRM Monograph Series and the
CRM Proceedings and Lecture
Notes. These collections include
works by prominent mathematicians,
some of them Fields medallists.
On the other hand Springer
publishes and distributes the
CRM Series in Mathematical
Physics and includes some CRM
titles in the collection Lecture
Notes in Statistics. Moreover
the CRM publishes and distributes
monographs, proceedings, lecture
notes, software, and videos
(in French or English).
15
Mathematics This program includes the following
of Planet Earth 2013 four themes.
• A planet to discover
oceans, meteorology and climate,
mantle processes, natural
the program Mathematics
resources, celestial mechanics
The CRM proposed
of Planet Earth 2013, • A planet supporting life
which now involves around
ecology, biodiversity, evolution
• A planet organized by humans
political, economic, social, and
financial systems; organization
all over the world and is one of
of transport and communications
networks; management of
the greatest scientific enterprises
resources; energy
100 organizations from
of the beginning
of the XXIst century.
• A planet at risk
climate change, sustainable
development, epidemics, invasive
species, natural disasters
Special
programs and
collaborations
planet earth 2013
16
The Centre National de la
Recherche Scientifique (CNRS),
a French institution, recently
created an Unité Mixte Internationale at the CRM. This unit will
foster and focus the many relationships that already exist between
mathematicians from France and
Québec. Professor Laurent
Habsieger is the new director of
the Unité Mixte Internationale.
Laurent Habsieger
Graphic Design: Neograf.ca
I like the