ECM-2012, Krakow: Abstracts and titles

98 Pages·2012·0.421 MB·English

Abstracts
&
Titles
6th European
Congress of Mathematics
Kraków 2012

Contents
Introduction 7
1 Plenary Lectures 9
Adrian Constantin 9
Camillo De Lellis 10
Herbert Edelsbrunner 11
Misha Gromov 12
Christopher Hacon 13
David Kazhdan 14
Tomasz Łuczak 15
Sylvia Serfaty 16
Saharon Shelah 17
Michel Talagrand 19
2 Invited Lectures 21
Anton Alekseev 21
Kari Astala 21
Jean Bertoin 22
Serge Cantat 22
Vicent Caselles 23
Alessandra Celletti 23
Pierre Colmez 24
Alessio Corti 24
Amadeu Delshams 25
Hélène Esnault 25
Alexander A. Gaifullin 25
Isabelle Gallagher 26
Olle Häggström 26
Martin Hairer 27
Nicholas J. Higham 28
Arieh Iserles 28
Alexander S. Kechris 29
Bernhard Keller 29
Sławomir Kołodziej 29
Gady Kozma 30
Frank Merle 30
Andrey Mironov 31
4 Contents
David Nualart 31
Alexander Olevskii 32
Leonid Parnovski 32
Florian Pop 33
Igor Rodnianski 33
Zeév Rudnick 33
Benjamin Schlein 34
Piotr Śniady 34
Andrew Stuart 35
Vladimír Sveřák 35
Stevo Todorčević 35
3 Special Lectures 37
Andrzej Pelczar Memorial Lecture 37
Alan Turing Centenary Lecture 37
Mathematics for the Planet Earth 38
4 Panel Discussions 39
EuDML: Accessing Europe’s mathematical treasures 39
Financing of mathematical research 39
Redressing the gender imbalance in mathematics: strategies and
outcomes 40
The role of mathematics in the emerging economies 40
“Solidfindings”inMathematicsEducation;proposalsanddiscussion 40
What is expected from European learned societies? 41
5 Mini-symposia 43
25 Years of Quantum Groups: From Definition to Classification 43
Absolute Arithmetic and F -geometry 43
1
Applied and Computational Algebraic Topology 43
Arithmetic Geometry 44
Bachelier Finance Society: Mathematical Finance 44
Braids and Configuration Spaces 44
Computational Dynamics and Computer Assisted Proofs 45
Continuous Real Rational Functions and Related Topics 45
Differential Algebra and Galois Theory 45
Discrete Structures in Algebra, Geometry, Topology, and Com-
puter Science 46
Fluid Dynamics 46
Geometric and Quantitative Rigidity 46
Contents 5
How Mathematics Illuminates Biology 47
Hyperbolic Conservation Laws 47
Implicitly Constituted Material Models: Modeling and Analysis 47
Infinite-dimensional Dynamical Systems with Time Delays 48
Knot Theory and its Ramification 48
Matchbox Dynamics 48
On Solutions to the Euler Equations of Incompressible Fluids 49
Optimal Stopping and Applications 49
Probabilistic Methods for Partial Differential Equations 49
Progress in ‘Chemical Reaction Network Theory’ 50
Semigroups of Operators: Theory and Applications 50
Stochastic Models in Biosciences and Climatology 50
6 Satellite Thematic Sessions 51
AlgebraicandGeometricMethodsinNonlinearPDEs,Mechanics
and Field Theory 51
Anisotropic Parabolic Problems and their Applications 51
Combinatorics 52
Delay Equations in Biomedical Applications 52
Geometric Methods in Calculus of Variations 53
Geometric Topology 53
Geometry in Dynamics 54
Homotopy Theory 55
Infinite Dimensional Dynamical Systems with Time Delays 56
Integrable Systems 56
Knot Theory and its Ramification 57
Mathematical Physics and Developments in Algebra 58
Optimal Stopping and Applications 58
Quasiconformal Mappings and Complex Dynamical Systems 59
Special Classes of Hilbert Space Operators 60
7 Research Posters 61
List of lectures 83
Statistics 92
Index 93
Scientific Committee
Chair Institute of Mathematics of the Academy of Sciences of
Eduard Feireisl ( ),
theCzechRepublic(CZ)
ICREA&UniversitatdeBarcelona(ES)
JoanBagaria,
King’sCollegeLondon(UK)
BrianDavies,
UniversitadiRoma“LaSapienza”(IT)
CorradoDeConcini,
UniversityDuisburg-Essen(DE)
GerhardFrey,
EidgenössischeTechnischeHochschuleZürich(CH)
SaravandeGeer,
MoscowStateUniversity(RU)
SabirGusein-Zade,
NorwegianUniversityofScienceandTechnology,Trondheim(NO)
HelgeHolden,
UniversityParis11(Paris-Sud,Orsay)(FR)
Jean-FrancoisLeGall,
UniversityofOxford(UK)
PhilipK.Maini,
JagiellonianUniversityinKraków(PL)
MarianMrozek,
UniversitätBonn(DE)
FelixOtto,
UniversidaddeValladolid(ES)
JesusSanz-Serna,
CWI&VrijeUniversiteitAmsterdam(NL)
JanH.vanSchuppen,
TelAvivUniversity(IL)
MishaSodin,
InstitutdeMathématiquesdeJussieu,CNRS,Paris(FR)
ClaireVoisin,
Poster Committee
Chair JagiellonianUniversityinKraków(PL)
RobertWolak( ),
Secretary JagiellonianUniversityinKraków(PL)
SylwiaBarnaś( ),
JagiellonianUniversityinKraków(PL)
SławomirRams,
JagiellonianUniversityinKraków(PL)
KamilRusek,
Executive Organizing Committee
Chair UniversityofWarsaw(PL)
StefanJackowski( ),
Vice-chair JagiellonianUniversityinKraków(PL)
ZbigniewBłocki( ),
MilitaryUniversityofTechnology,Warszawa(PL)
KrystynaJaworska,
AdamMickiewiczUniversity,Poznań(PL)
WacławMarzantowicz,
JagiellonianUniversityinKraków(PL)
PiotrTworzewski,
JagiellonianUniversityinKraków(PL)
RobertWolak,
Editorial Committee
Chair UniversityofWarsaw(PL)
PawełStrzelecki( ),
UniversityofWarsaw(PL)
RafałLatała,
Secretary JagiellonianUniversityinKraków(PL)
LeszekPieniążek( ),
AdamMickiewiczUniversity,Poznań(PL)
AndrzejRuciński,
UniversityofWrocław(PL)
JacekŚwiątkowski,
UniversityofWarsaw(PL)
DariuszWrzosek,
Vice-Chair UniversityofWarsaw(PL)
PiotrZakrzewski( ),
Typesetting
LeszekPieniążek
Cover design
Podpunkt,Warszawa
Printing
Esus,Poznań
Introduction
This brochure contains information about the scientific programme of the 6.
European Congress of Mathematics:
•
Abstracts of plenary lectures with short vitae of speakers
•
Abstracts of invited and special lectures
•
Titles of presentations in panel discussions
•
Titles of talks in mini-symposia
•
Titles of talks in Satellite Thematic Sessions
•
Titles of research posters
A list of all lectures and talks grouped according to subject classification is
included for convenience.
Thescheduleofall6ECMactivitiesisprovidedinthebrochure“Programme
& Information”.
Abstracts and timetable of the lectures delivered by the prize winners are
collectedinaseparatebrochurewhichwillbedistributedrightaftertheopen-
ning ceremony at which the prizes will be presented.
The plenary speakers and the invited speakers were nominated by the Sci-
entific Committee of the 6ECM, formed by the Executive Committee of the
European Mathematical Society. The same Committee selected the mini-
symposia from proposals submitted in an open call via the 6ECM website.
Note that a Mini-symposium is a special session consisting of four coordi-
nated presentations on a selected topic. Speakers at a mini-symposium are
invited by its organizers.
Two of the three special lectures: The Alan Turing Centennial Lecture and
on the Mathematics of the Planet Earth (MPE) were proposed by the Exec-
utive Committee of the EMS. The lecture on MPE will be delivered at the
special open London Mathematical Society meeting.
The first special lecture: the Andrzej Pelczar Memorial Lecture was es-
tablished by the Polish Mathematical Society (PTM). It will be followed by
award of the PTM annual scientific prizes.
Theproposalsforpostersweresubmittedinanopencallthroughthe6ECM
website and the Poster Committee nominated by the Executive Organizing
Committee (EOC) made the selections with the help of many referees. All
proposals (abstracts of posters) were refereed.
EOC suggested the organization of some panel discussions and asked se-
lectedmathematicianstobecomechairsandtoinvitetheotherpanelists. Some
other panel discussions were proposed and organised spontaneously.
8 Introduction
The Satellite Thematic Sessions (STS) were chosen by the EOC from pro-
posalssubmittedinanopencallviathe6ECMwebsite. TheSTSareintended
to serve as extensions of mini-symposia programme and they will be held in
the afternoons during the scientific activities of the 6ECM and whole day on
Sunday, July 1.
The abstracts were edited by the Editorial Committee of the 6ECM Pro-
ceedings.
1 Plenary Lectures
Some mathematical aspects of water waves
[email protected]
Adrian Constantin
King’sCollege,London(UK)
UniversityofVienna(AT)
We survey recent advances on two fundamental aspects:
•
Whilewatchingtheseaitisoftenpossibletotraceawaveasitpropagateson
the water surface. Contrary to a possible first impression, what one observes
traveling across the sea is not the water but a pattern (pulse of energy).
A basic question in hydrodynamics concerns the particle paths beneath a
traveling surface water wave. In the absence of an underlying current, one
can give a qualitative description of the trajectories. The proof relies on an
interplay of methods from harmonic function theory, dynamical systems and
elliptic partial differential equations.
•
Of all the magnificent scenes presented by water waves, breaking is surely
amongthemostimpressive. Althoughthemathematicaldescriptionofthepro-
cesses of breaking could hardly be regarded as satisfactory, some theoretical
investigations offer insight. We will discuss breaking waves based on the
Camassa–Holm equation which arises as an approximation to the governing
equations for water waves in the shallow water regime of waves of moderate
amplitude.
Both themes illustrate that an appreciation of mathematical rigor and el-
egance, combined with the power of meaningful abstraction, often leads to
breakthroughs in physical insight, while mathematics draws considerable in-
spiration and stimulation from physics.
AMSMSC2010: Primary35Q31,35Q35;Secondary34C99,31A05.
graduatedinmathematicsfromtheUniversityof
AdrianConstantin
Nicein1992,anddefendedhisPhDinmathematicsin1996atthe
Courant Institute of Mathematical Sciences, under the supervision
ofHenryP.McKeanandPeterD.Lax. Heobtainedhishabilitation
in1999fromtheUniversityofZürich.
In2000ConstantinwasappointedChairofMathematicsatLund
University. During 2004–2008 he held the Erasmus Smith’s Chair
ofMathematics(founded1762)attheTrinityCollegeinDublin. He
has been Professor of Mathematics at the University of Vienna (Austria) since 2008,
andisthecurrentholderoftheChairinAnalysisatKing’sCollegeLondon.
Adrian Constantin’s research interests are focused on partial differential equations
and their applications in physics. He was awarded several research prizes, includ-
ing the Benedetto Sciarra prize of the Scuola Normale Superiore di Pisa in 1994,
the Göran Gustafsson prize of the Royal Swedish Academy of Sciences in 2005, the
Friedrich Bessel prize of the Humboldt foundation in 2007, and the Fluid Dynamics
ResearchprizeoftheJapaneseSocietyofFluidMechanics(2008).
10 Plenary Lectures
Dissipative solutions of the Euler equations
[email protected]
Camillo De Lellis
UniversitätZürich(CH)
The incompressible Euler equations were derived more than 250 years ago
byEulertodescribethemotionofaninviscidincompressiblefluid. Itisknown
sincethepioneeringworksofSchefferandShnirelmanthattherearenontrivial
distributional solutions to these equations which are compactly supported in
spaceandtime. Iftheyweretomodelthemotionofarealfluid, wewouldsee
it suddenly start moving after staying at rest for a while, without any action
by an external force. A celebrated theorem by Nash and Kuiper shows the
existence of C1 isometric embeddings of a fixed flat rectangle in arbitrarily
smallballsofthethreedimensionalspace. Youshouldthereforebeabletoput
a fairly large piece of paper in a pocket of your jacket without folding it or
crumpling it.
In a first joint work with László Székelyhidi we pointed out that these two
counterintuitivefactssharemanysimilarities. Thishasbecomeevenmoreap-
parentinamorerecentresultofours,whichprovestheexistenceofcontinuous
solutions which dissipate the kinetic energy. Our theorem might be regarded
as a first step towards a conjecture of Lars Onsager, which in his 1949 paper
about the theory of turbulence asserted the existence of dissipative Hölder
solutions.
AMSMSC2010: 35Q31.
studiedmathematicsattheScuolaNormaleSu-
CamilloDeLellis
periore di Pisa from 1995 to 2002, where he graduated under the
supervisionofLuigiAmbrosio. Since2005heholdsafullprofessor-
shipattheUniversityofZürich.
DeLellis’researchinterestslieingeometricanalysisandpartial
differential equations. He is particularly well known for his works
ingeometricmeasuretheoryandontheincompressibleEulerequa-
tions. In 2009 he has received the Stampacchia medal, awarded
every three years by the Italian Mathematical Union in recognition of outstanding
contributions to the field of calculus of variations and related applications, and was
aninvitedspeakerattheInternationalCongressofMathematiciansin2010.