Organisateur/Organizer

Henri Darmon (Université McGill)


Archives

Colloque de mathématiques CRM-ISM
2017-2018
2016-2017
2015-2016
2014-2015
2013-2014
2012-2013
2011-2012
2010-2011
2009-2010
2008-2009
2007-2008
2006-2007
2005-2006
2004-2005
2003-2004
2002-2003

Colloque de statistique CRM-ISM-GERAD
2013-2014
2012-2013
2011-2012
2010-2011
2009-2010
2008-2009

2018 - 2019

Calendrier / Calendar

MONTRÉAL



Date Heure/Time : Le vendredi 7 septembre 2018 - 16:00

Lieu/Venue : CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6254

Conférencier/Speaker : Kasia Rejzner, University of York

Titre/Title : Mathematical challenges in constructing quantum field theory models

Resume/Abstract :
This talk is an overview of algebraic quantum field theory (AQFT) and its perturbative generalization: pAQFT. Both are axiomatic systems meant to provide foundations for quantum field theory (the theory underlying particle physics). I will explain what is the current status of constructing physically relevant models in both approaches and present future perspectives. The most recent results include applications of pAQFT in Yang-Mills theories and effective quantum gravity, as well as some progress in understanding how to go beyond the perturbation theory.


Date Heure/Time : Le vendredi 14 septembre 2018 - 16:00

Lieu/Venue : CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6254

Conférencier/Speaker : Sylvia Serfaty, Courant Institute, NYU

Titre/Title : Systems of points with Coulomb interactions

Resume/Abstract :
Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and they give rise to a variety of questions pertaining to analysis, Partial Differential Equations and probability. We will first review these motivations, then present the ''mean-field'' derivation of effective models and equations describing the system at the macroscopic scale. We then explain how to analyze the next order behavior, giving information on the configurations at the microscopic level and connecting with crystallization questions, and finish with the description of the effect of temperature.


Date Heure/Time : Le vendredi 21 septembre 2018 - 16:00

Lieu/Venue : UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115

Conférencier/Speaker : Ezra Miller, Duke University

Titre/Title : Algebraic structures for topological summaries of data

Resume/Abstract :
This talk introduces an algebraic framework to encode, compute, and analyze topological summaries of data. The main motivating problem, from evolutionary biology, involves statistics on a dataset comprising images of fruit fly wing veins, which amount to embedded planar graphs with varying combinatorics. Additional motivation comes from statistics more generally, the goal being to summarize unknown probability distributions from samples. The algebraic structures for topological summaries take their cue from graded polynomial rings and their modules, but the theory is complicated by the passage from integer exponent vectors to real exponent vectors. The key to making the structures practical for data science applications is a finiteness condition that encodes topological tameness -- which occurs in all modules arising from data -- robustly, in equivalent combinatorial and homological algebraic ways. Out of the tameness condition surprisingly falls much of ordinary commutative algebra, including syzygy theorems and primary decomposition.


Date Heure/Time : Le vendredi 28 septembre 2018 - 16:00

Lieu/Venue : McGill University, Burnside Hall, salle 1104, 805 rue Sherbrooke O.

Conférencier/Speaker : Hans-Otto Walther, Universität Giessen

Titre/Title : A delay differential equation with a solution whose shortened segments are dense

Resume/Abstract :
Simple-looking autonomous delay differential equations $$x'(t)=f(x(t-r))$$ with a real function $f$ and single time lag $r>0$ can generate complicated (chaotic) solution behaviour, depending on the shape of $f$. The same could be shown for equations with a variable, state-dependent delay $r=d(x_t)$, even for the linear case $f(\xi)=-\alpha\,\xi$ with $\alpha>0$. Here the argument $x_t$ of the {\it delay functional} $d$ is the history of the solution $x$ between $t-r$ and $t$ defined as the function $x_t:[-r,0]\to\mathbb{R})$ given by $x_t(s)=x(t+s)$. So the delay alone may be responsible for complicated solution behaviour. In both cases the complicated behaviour which could be established occurs in a thin dust-like invariant subset of the infinite-dimensional Banach space or manifold of functions $[-r,0]\to\mathbb{R}$ on which the delay equation defines a nice semiflow. The lecture presents a result which grew out of an attempt to obtain complicated motion on a larger set with non-empty interior, as certain numerical experiments seem to suggest. For some $r>1$ we construct a delay functional $d:Y\to(0,r)$, $Y$ an infinite-dimensional subset of the space $C^1([-r,0],\mathbb{R})$, so that the equation $$x'(t)=-\alpha\,x(t-d(x_t))$$ has a solution whose {\it short segments} $x_t|_{[-1,0]}$, $t\ge0$, are dense in the space $C^1([-1,0],\mathbb{R})$. This implies a new kind of complicated behaviour of the flowline $[0,\infty)\ni t\mapsto x_t\in C^1_r$. Reference: H. O. Walther, {\em A delay differential equation with a solution whose shortened segments are dense}.\\ J. Dynamics Dif. Eqs., to appear.


Date Heure/Time : Le vendredi 5 octobre 2018 - 16:00

Lieu/Venue : CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6254

Conférencier/Speaker : Mireille Bousquet-Mélou, CNRS - Université de Bordeaux

Titre/Title : Counting lattice walks confined to cones

Resume/Abstract :
The study of lattice walks confined to cones is a very lively topic in combinatorics and in probability theory, which has witnessed rich developments in the past 20 years. In a typical problem, one is given a finite set of allowed steps S in Z^d, and a cone C in R^d. Clearly, there are |S|^n walks of length n that start from the origin and take their steps in S. But how many of them remain the the cone C? One of the motivations for studying such questions is that lattice walks are ubiquitous in various mathematical fields, where they encode important classes of objects: in discrete mathematics (permutations, trees, words...), in statistical physics (polymers...), in probability theory (urns, branching processes, systems of queues), among other fields. The systematic study of these counting problems started about 20 years ago. Beforehand, only sporadic cases had been solved, with the exception of walks with small steps confined to a Weyl chamber, for which a general reflection principle had been developed. Since then, several approaches have been combined to understand how the choice of the steps and of the cone influence the nature of the counting sequence a(n), or of the the associated series A(t)=\sum a(n) t^n. For instance, if C is the first quadrant of the plane and S only consists of "small" steps, it is now understood when A(t) is rational, algebraic, or when it satisfies a linear, or a non-linear, differential equation. Even in this simple case, the classification involves tools coming from an attractive variety of fields: algebra on formal power series, complex analysis, computer algebra, differential Galois theory, to cite just a few. And much remains to be done, for other cones and sets of steps. This talk will survey these recent developments, and conclude a series of talks by the author, in the framework of the Aisenstadt chair.


Date Heure/Time : Le vendredi 12 octobre 2018 - 16:00

Lieu/Venue : CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6254

Conférencier/Speaker : David Haziza, Univ. de Montréal - Lauréat 2018 du Prix CRM-SSC

Titre/Title : Robust estimation in the presence of influential units for skewed finite and infinite populations

Resume/Abstract :
Many variables encountered in practice (e.g., economic variables) have skewed distributions. The latter provide a conducive ground for the presence of influential observations, which are those that have a drastic impact on the estimates if they were to be excluded from the sample. We examine the problem of influential observations in a classical statistic setting as well as in a finite population setting that includes two main frameworks: the design-based framework and the model-based framework. Within each setting, classical estimators may be highly unstable in the presence of influential units. We propose a robust estimator of the population mean based on the concept of conditional bias of a unit, which is a measure of influence. The idea is to reduce the impact of the sample units that have a large conditional bias. The proposed estimator depends on a cut-off value. We suggest selecting the cut-off value that minimizes the maximum absolute estimated conditional bias with respect to the robust estimator. The properties of the proposed estimator will be discussed. Finally, the results of a simulation study comparing the performance of several estimators in terms of bias and mean square error will be presented.


Date Heure/Time : Le vendredi 19 octobre 2018 - 16:00

Lieu/Venue : CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 1140

Conférencier/Speaker : Ariel Zhitnitsky, UBC - Lauréat 2018 du Prix ACP-CRM

Titre/Title : Vacuum Energy of the Universe and nontrivial topological sectors in Quantum Field Theory

Resume/Abstract :
I discuss a new scenario for early cosmology when  the inflationary de Sitter phase emerges dynamically. This genuine quantum effect occurs as a result of   dynamics of the topologically nontrivial sectors in a   strongly coupled non-abelian gauge theory   in an expanding universe.  I argue that the key element for this idea to work is the presence of nontrivial holonomy in strongly coupled gauge theories. The effect is global in nature, non-analytical in coupling constant,  and cannot be formulated in terms of a gradient expansion in an effective local field theory. I explain the basic ideas of this framework using a simplified 2D quantum field theory where precise computations can be   carried out in theoretically controllable way. I move on to generalize the computations to  4D non-abelian gauge field theories.  The last (and most important  for cosmological applications) part of my talk is based on recent paper  [arXiv:1709.09671].  


Date Heure/Time : Le vendredi 26 octobre 2018 - 16:00

Lieu/Venue : CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6254

Conférencier/Speaker : David P. Ruelle, Institut des Hautes Études Scientifiques

Titre/Title : A generalized detailed balance relation

Resume/Abstract :
The transition probabilities of reactions J -> K and K -> J in a thermal bath are related because of the time reversal symmetry of fundamental physical laws. The relation is known as detailed balance relation. We study the problems that arise in obtaining a rigorous proof of detailed balance, using deterministic rather than Markovian dynamics. J. Englands’ biological applications of detailed balance are briefly considered.


Date Heure/Time : Le vendredi 2 novembre 2018 - 16:00

Lieu/Venue : CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 1355

Conférencier/Speaker : Benjamin Rossman, University of Toronto - Lauréat 2018 du Prix André-Aisenstadt

Titre/Title : The complexity of detecting cliques and cycles in random graphs

Resume/Abstract :
A strong form of the P ≠ NP conjecture holds that no algorithm faster than n^{O(k)} solves the k-clique problem with high probability when the input is an Erdös–Rényi random graph with an appropriate edge density. Toward this conjecture, I will describe a line of work lower-bounding the average-case complexity of k-clique (and other subgraph isomorphism problems) in weak models of computation: namely, restricted classes of boolean circuits and formulas. Along the way I will discuss some of the history and current frontiers in Circuit Complexity. Joint work with Ken-ichi Kawarabayashi, Yuan Li and Alexander Razborov.


Date Heure/Time : Le vendredi 9 novembre 2018 - 16:00

Lieu/Venue : McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

Conférencier/Speaker : Akshay Venkatesh, IAS

Titre/Title : À venir

Resume/Abstract :
À venir / Coming soon


Date Heure/Time : Le vendredi 16 novembre 2018 - 16:00

Lieu/Venue : CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6254

Conférencier/Speaker : Svetlana Jitomirskaya, UC Irvine

Titre/Title : Conférence de la Chaire Aisenstadt

Resume/Abstract :
À venir / Coming soon


Date Heure/Time : Le vendredi 30 novembre 2018 - 16:00

Lieu/Venue : McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

Conférencier/Speaker : Marcin Sabok, McGill University

Titre/Title : À venir

Resume/Abstract :
À venir / Coming soon


Date Heure/Time : Le vendredi 25 janvier 2019 - 16:00

Lieu/Venue : CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6254

Conférencier/Speaker : Vadim Kaloshin, University of Maryland

Titre/Title : Conférence Nirenberg du CRM en analyse géométrique

Resume/Abstract :
À venir / Coming soon


Date Heure/Time : Le vendredi 8 février 2019 - 16:00

Lieu/Venue : À venir

Conférencier/Speaker : Viktor Ginzburg, University of California, Santa Cruz

Titre/Title : À venir

Resume/Abstract :
À venir / Coming soon


Date Heure/Time : Le vendredi 15 février 2019 - 16:00

Lieu/Venue : McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

Conférencier/Speaker : Fanny Kassel, CNRS, Institut des Hautes Études Scientifiques

Titre/Title : À venir

Resume/Abstract :
À venir / Coming soon


Date Heure/Time : Le vendredi 1 mars 2019 - 16:00

Lieu/Venue : McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

Conférencier/Speaker : Alex Lubotzky, The Hebrew University of Jerusalem

Titre/Title : À venir

Resume/Abstract :
À venir / Coming soon


Date Heure/Time : Le vendredi 15 mars 2019 - 16:00

Lieu/Venue : McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

Conférencier/Speaker : Shmuel Weinberger, University of Chicago

Titre/Title : À venir

Resume/Abstract :
À venir / Coming soon


Date Heure/Time : Le vendredi 22 mars 2019 - 16:00

Lieu/Venue : UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115

Conférencier/Speaker : Emmy Murphy, Northwestern University

Titre/Title : À venir

Resume/Abstract :
À venir / Coming soon


Date Heure/Time : Le vendredi 12 avril 2019 - 16:00

Lieu/Venue : McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

Conférencier/Speaker : Nicolas Bergeron, Institut de Mathématiques de Jussieu - Paris Rive Gauche

Titre/Title : Enlacement dans les fibrés en tores et fonctions L de Hecke

Resume/Abstract :
Les espaces obtenus comme suspension d'un difféomorphisme linéaire du tore sont parmi les plus simples et jolis exemples de variétés de dimension 3. Après les avoir présentés, notamment grâce à des animations réalisées par Jos Leys, je chercherai à comprendre comment s'y enlacent les orbites périodiques. Nous verrons que les nombres d'enlacement ainsi obtenus, nombres rationnels par définition, sont aussi naturellement égaux à certaines valeurs spéciales de fonctions L de Hecke. Convenablement généralisé ce point de vue permet de retrouver des théorèmes classiques mais aussi de démontrer de nouveaux théorèmes de rationalité pour ces valeurs spéciales. Le matériel de cet exposé est extrait d'un travail en cours avec Pierre Charollois, Luis Garcia et Akshay Venkatesh.


Date Heure/Time : Le vendredi 26 avril 2019 - 16:00

Lieu/Venue : McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

Conférencier/Speaker : Alan W. Reid, Rice University

Titre/Title : À venir

Resume/Abstract :
À venir / Coming soon


Date Heure/Time : Le vendredi 3 mai 2019 - 16:00

Lieu/Venue : McGill University, Burnside Hall , 805 O., rue Sherbrooke, salle 1104

Conférencier/Speaker : Lenya Ryzhik, Stanford University

Titre/Title : À venir

Resume/Abstract :
À venir / Coming soon


Date Heure/Time : Le vendredi 17 mai 2019 - 16:00

Lieu/Venue : UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115

Conférencier/Speaker : Lucia Caporaso, Università Roma Tre

Titre/Title : À venir

Resume/Abstract :
À venir / Coming soon