# 2019 - 2020

# Calendrier / Calendar

# MONTRÉAL

**Date Heure/Time**: Le vendredi 30 août 2019 - 16:00

**Lieu/Venue**: UQAM, Pavillon Sherbrooke, 200, rue Sherbrooke ouest, salle SH-3620

**Conférencier/Speaker**: Ciprian Manolescu, UCLA - Chaire Aisenstadt 2019

**Titre/Title**: Khovanov homology, 3-manifolds, and 4-manifolds

**Resume/Abstract**:

Khovanov homology is an invariant of knots in R^3. A major open problem is to extend its definition to knots in other three-manifolds, and to understand its relation to surfaces in 4-manifolds. I will discuss some partial progress in these directions, from different perspectives (gauge theory, representation theory, sheaf theory). In the process I will also review some of the topological applications of Khovanov homology.

**Date Heure/Time**: Le vendredi 13 septembre 2019 - 16:00

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

**Conférencier/Speaker**: Brent Pym, McGill University

**Titre/Title**: Multiple zeta values in deformation quantization

**Resume/Abstract**:

The subject of "deformation quantization" originated as a mathematical abstraction of the passage from classical to quantum mechanics: starting from a classical phase space (i.e. a Poisson manifold), we deform the ordinary multiplication of functions to produce a noncommutative ring, which serves as the algebra of quantum observables. Over the years, the theory has evolved from its physical origins to take on a mathematical life of its own, with rich connections to representation theory, topology, graph theory, number theory and more. I will give an introduction to the subject and explain how the quantization process is inextricably linked, via a formula of Kontsevich, to special values of the Riemann zeta function, and their generalizations known as multiple zeta values.

**Date Heure/Time**: Le vendredi 20 septembre 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**: Groups' approximation, stability and high dimensional expanders

**Resume/Abstract**:

Several well-known open questions (such as: are all groups sofic or hyperlinear?) have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, some of these versions, showing that there exist finitely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2)norm. The strategy is via the notion of "stability": some higher dimensional cohomology vanishing phenomena is proven to imply stability and using higher dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. All notions will be explained. Based on joint works with M, De Chiffre, L. Glebsky and A. Thom and with I. Oppenheim.

**Date Heure/Time**: Le jeudi 26 septembre 2019 - 16:00

**Lieu/Venue**: Université de Montréal, Pavillon Roger-Gaudry, salle M-415

**Conférencier/Speaker**: Nassif Ghoussoub, UBC - Lauréat 2019 du Prix CRM-Fields-PIMS

**Titre/Title**: From Monge optimal transports to optimal Skorokhod embeddings

**Resume/Abstract**:

The optimal transportation problem, which originated in the work of Gaspard Monge in 1781, provides a fundamental and quantitave way to measure the distance between probability distributions. It has led to many successful applications in PDEs, Geometry, Statistics and Probability Theory. Recently, and motivated by problems in Financial Mathematics, variations on this problem were introduced by requiring the transport plans to abide by certain "fairness rules," such as following martingale paths. One then specifies a stochastic state process and a costing procedure, and minimize the expected cost over stopping times with a given state distribution. Recent work has uncovered deep connections between this type of constrained optimal transportation problems, the celebrated Skorokhod embeddings of probability distributions in Brownian motion, and Hamilton-Jacobi variational inequalities.

**Date Heure/Time**: Le vendredi 4 octobre 2019 - 16:00

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

**Conférencier/Speaker**: Johanna Nešlehová, McGill University - Lauréate 2019 du Prix CRM-SSC

**Titre/Title**: La queue, la tuile, le bris d’égalité et leur rôle dans les modèles de dépendance

**Resume/Abstract**:

La modélisation de la dépendance entre variables aléatoires est omniprésente en statistique. S’agissant d’événements rares à fort impact, tels que des orages violents, des inondations ou des vagues de chaleur, la question revêt une grande importance pour la gestion des risques et pose des défis théoriques. Une approche hautement flexible et prometteuse s’appuie sur la théorie des valeurs extrêmes, la modélisation par copules et l’inférence fondée sur les rangs. Je présenterai trois avancées récentes dans ce domaine. Nous nous intéresserons d’abord à la prise en compte de la dépendance en régime moyen, lorsque les modèles asymptotiques de valeurs extrêmes ne conviennent pas. Nous verrons ensuite quoi faire lorsque le nombre de variables est grand et comment une structure de modèle hiérarchique peut être apprise à partir de matrices de corrélation de rangs de grande taille. Enfin, je ne résisterai pas à l’envie de vous initier à l’univers complexe de l’inférence basée sur les rangs pour les données discrètes ou mixtes.

**Date Heure/Time**: Le vendredi 11 octobre 2019 - 16:00

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

**Conférencier/Speaker**: Ruth Misener, Imperial College

**Titre/Title**: Scoring positive semidefinite cutting planes for quadratic optimization via trained neural networks

**Resume/Abstract**:

Semidefinite programming relaxations complement polyhedral relaxations for quadratic optimization, but global optimization solvers built on polyhedral relaxations cannot fully exploit this advantage. We develop linear outer-approximations of semidefinite constraints that can be effectively integrated into global solvers for nonconvex quadratic optimization. The difference from previous work is that our proposed cuts are (i) sparser with respect to the number of nonzeros in the row and (ii) explicitly selected to improve the objective. A neural network estimator is key to our cut selection strategy: ranking each cut based on objective improvement involves solving a semidefinite optimization problem, but this is an expensive proposition at each Branch&Cut node. The neural network estimator, trained a priori of any instance to solve, takes the most time consuming computation offline by predicting the objective improvement for any cut.

**Date Heure/Time**: Le vendredi 18 octobre 2019 - 16:00

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

**Conférencier/Speaker**: Jacob Tsimerman, University of Toronto

**Titre/Title**: o-minimal GAGA and applications to Hodge theory

**Resume/Abstract**:

(joint with B.Bakker and Y.Brunebarbe) One very fruitful way of studying complex algebraic varieties is by forgetting the underlying algebraic structure, and just thinking of them as complex analytic spaces. To this end, it is a natural and fruitful question to ask how much the complex analytic structure remembers. One very prominent result is Chows theorem, stating that any closed analytic subspace of projective space is in fact algebraic. One notable consequence of this result is that a compact complex analytic space admits at most 1 algebraic structure - a result which is false in the non-compact case. This was generalized and extended by Serre in his famous GAGA paper using the language of cohomology. We explain how we can extend Chow's theorem and in fact all of GAGA to the non-compact case by working with complex analytic structures that are "tame" in the precise sense defined by o-minimality. This leads to some very general "algebraization" theorems, and we give applications to Hodge theory.

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

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

**Conférencier/Speaker**: Melanie Matchett Wood, UC Berkeley

**Titre/Title**: Coincidences in homological densities

**Resume/Abstract**:

For certain natural sequences of topological spaces, the kth homology group stabilizes once you go far enough out in the sequence of spaces. This phenomenon is called homological stability. Two classical examples of homological stability are the configuration space of n unordered distinct points in the plane, studied in the 60's by Arnold' and the space of (based) algebraic maps from CP^1 to CP^1 studied by Segal in the 70's. It turns out that the stable homology is the same in these two examples, and in this talk we explain that this is just the tip an iceberg--a subtle, but precise relationship between the values of stable of homology different sequences of spaces. To explain this relationship, which we discovered through an analogy to asymptotic counts in number theory, we introduce a new notion of homological density. This talk is on joint work with Benson Farb and Jesse Wolfson.

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

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

**Conférencier/Speaker**: Stephen Walker, University of Texas

**Titre/Title**: General Bayesian modeling

**Resume/Abstract**:

The work is motivated by the inflexibility of Bayesian modeling; in that only parameters of probability models are required to be connected with data. The idea is to generalize this by allowing arbitrary unknowns to be connected with data via loss functions. An updating process is then detailed which can be viewed as arising in at least a couple of ways - one being purely axiomatically driven. The further exploration of replacing probability model based approaches to inference with loss functions is ongoing. Joint work with Chris Holmes, Pier Giovanni Bissiri and Simon Lyddon.

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

**Lieu/Venue**: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6214

**Conférencier/Speaker**: Jaume Gomis, Lauréat 2019 du Prix CAP-CRM, Institut Périmètre de physique théorique

**Titre/Title**: Symmetries in topological quantum field theories

**Resume/Abstract**:

In this talk I will describe how to characterize symmetries of topological field theories and give a complete classification of symmetries in Abelian Topological Field Theories, uncovering a plethora of quantum symmetries in these theories and an intriguing connection to number theory

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

**Lieu/Venue**: CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 6214

**Conférencier/Speaker**: Yaniv Plan, University of British Columbia - Lauréat 2019 du Prix André-Aisnestadt

**Titre/Title**:

**Resume/Abstract**:

Random models lead to a precise and comprehensive theory of compressive sensing and matrix completion. The number of random linear measurements needed to recover a sparse signal, or a low-rank matrix, or, more generally, a structured signal, are now well understood. Indeed, this boils down to a question in random matrix theory: How well conditioned is a random matrix restricted to a fixed subset of R^n? We discuss recent work addressing this question in the sub-Gaussian case. Nevertheless, a practitioner with a fixed data set will wonder: Can they apply theory based on randomness? Is there any hope to get the same guarantees? We discuss these questions in compressive sensing and matrix completion, which, surprisingly, seem to have divergent answers.

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

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

**Conférencier/Speaker**: Donald Estep, Simon Fraser University

**Titre/Title**: Formulation and solution of stochastic inverse problems for science and engineering models

**Resume/Abstract**:

The stochastic inverse problem of determining probability structures on input parameters for a physics model corresponding to a given probability structure on the output of the model forms the core of scientific inference and engineering design. We describe a formulation and solution method for stochastic inverse problems that is based on functional analysis, differential geometry, and probability/measure theory. This approach yields a computationally tractable problem while avoiding alterations of the model like regularization and ad hoc assumptions about the probability structures. We present several examples, including a high-dimensional application to determination of parameter fields in storm surge models. We also describe work aimed at defining a notion of condition for stochastic inverse problems and tackling the related problem of designing sets of optimal observable quantities.

**Date Heure/Time**: Le vendredi 29 novembre 2019 - 16:00

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

**Conférencier/Speaker**: Persi Diaconis, Stanford University

**Titre/Title**: Shuffling and Group Representations

**Resume/Abstract**:

Picture n cards, numbered 1,2,...,n face down, in order, in a row on the table. Each time, your left hand picks a random card, your right hand picks a random card and the two cards are transposed. It is clear that 'after a while' the cards get all mixed up. How long does this take? In joint work with Mehrdad Shahshahani we analyzed this problem using the character theory of the symmetric group. The methods work for general measures on general compact groups. They mix probability, analysis, combinatorics and group theory (we need real formulas for the representations). I will try to explain all of this(along with some motivation for studying such problems) 'in English'. The answer, when n=52, is 'about 400'.

**Date Heure/Time**: Le vendredi 17 janvier 2020 - 14:00

**Lieu/Venue**: Pavillon André-Aisenstadt, Université de Montréal, salle 6214-6254

**Conférencier/Speaker**: Éva Tardos, Cornell University

**Titre/Title**: Learning in Games

**Resume/Abstract**:

Selfish behavior can often lead to suboptimal outcome for all participants, a phenomenon illustrated by many classical examples in game theory. Over the last decade we developed good understanding on how to quantify the impact of strategic user behavior on the overall performance in many games (including traffic routing as well as online auctions). In this talk we will focus on games where players use a form of learning that helps them adapt to the environment, and consider two closely related questions: What are broad classes of learning behaviors that guarantee high social welfare in games, and are these results robust to situations when game or the population of players is dynamically changing.

**Date Heure/Time**: Le vendredi 24 janvier 2020 - 16:00

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

**Conférencier/Speaker**: Olivier Lafitte, Unité Mixte Internationale – Centre de recherches mathématiques (UMI-CRM).

**Titre/Title**: Propagation des ondes et diffraction par un obstacle: résultats utilisant l’analyse microlocale

**Resume/Abstract**:

Nous décrirons des résultats pour la propagation des ondes, et nous pourrons donner des preuves de résultats classiques d’optique géométriques, de théorie géométrique de la diffraction et de propagation et réflexions des singularités d’ondes scalaires ou vectorielles (supposant le bord analytique dans le cas de la réflexion et du calcul des rayons rampants)

**Date Heure/Time**: Le vendredi 31 janvier 2020 - 16:00

**Lieu/Venue**: HEC Montréal, 3000, chemin de la Côte-Sainte-Catherine, salle Béton Grilli

**Conférencier/Speaker**: Ana-Maria Staicu, North Carolina State University

**Titre/Title**: Longitudinal functional regression: tests of significance

**Resume/Abstract**:

We consider longitudinal functional regression, where, for each subject, the response consists of multiple curves observed at different time visits. We discuss tests of significance in two general settings. First, when there are no additional covariates, we develop a hypothesis testing methodology for formally assessing that the mean function does not vary over time. Second, in the presence of other covariates, we propose a testing procedure to determine the significance of the covariate's time-varying effect formally. The methods account for the complex dependence structure of the response and are computationally efficient. Numerical studies confirm that the testing approaches have the correct size and are have a superior power relative to available competitors. We illustrate the methods on a real data application.

**Date Heure/Time**: Le vendredi 7 février 2020 - 16:00

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

**Conférencier/Speaker**: Eyal Z. Goren , McGill University

**Titre/Title**: Complex multiplication - old and new

**Resume/Abstract**:

The theory of complex multiplication is more than a century old; its origins date back to Klein, Hilbert, Kummer, Weber, Deuring and many others. It has been instrumental in the development of class field theory and algebraic number theory. Yet, more than a century later we find new theorems that are truly surprising. I will start with this historical perspective and try to position some of these new developments in the light of the André-Oort conjecture - a conjecture in the area of Shimura varieties that was recently resolved by Tsimerman, building on ideas of Edixhoven, Pila, Wilkie and Zannier. The resolution rests on the averaged Colmez conjecture, a conjecture that addresses the arithmetic complexity of abelian varieties with complex multiplication, which was proved by Andreatta-Howard-Madapusi Pera and the speaker, and, independently, by Yuan-Zhang

**Date Heure/Time**: Le vendredi 21 février 2020 - 16:00

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

**Conférencier/Speaker**: Steve Kudla, University of Toronto

**Titre/Title**: Arithmetic Theta Series

**Resume/Abstract**:

I will recount a family history of theta series through several generations. Theta series for positive definite integral quadratic forms provide some of the most classical examples of elliptic modular forms and their Siegel modular variants. Analogous series were defined by Siegel and Maass for lattices with indefinite quadratic forms say with signature (p,q). These series are no longer holomorphic and depend on an additional variable in the Grassmannian of negative q-planes, i.e., the symmetric space for the orthogonal group O(p,q). Motivated by work of Hirzebruch and Zagier on the generating series for curves on Hilbert modular surfaces, Millson and I constructed a theory of theta series valued in the cohomology of certain locally symmetric spaces -- geometric theta series. More recently, a theory of arithmetic theta series has been emerging, theta series valued in the Chow groups or arithmetic Chow groups of the integral models of certain Shimura varieties.

**Date Heure/Time**: Le vendredi 28 février 2020 - 16:00

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

**Conférencier/Speaker**: Yang Feng, NYU

**Titre/Title**: Neyman-Pearson classification: parametrics and sample size requirement

**Resume/Abstract**:

The Neyman-Pearson (NP) paradigm in binary classification seeks classifiers that achieve a minimal type II error while enforcing the prioritized type I error controlled under some user-specified level alpha. This paradigm serves naturally in applications such as severe disease diagnosis and spam detection, where people have clear priorities among the two error types. Recently, Tong, Feng and Li (2018) proposed a nonparametric umbrella algorithm that adapts all scoring-type classification methods (e.g., logistic regression, support vector machines, random forest) to respect the given type I error (i.e., conditional probability of classifying a class 0 observation as class 1 under the 0-1 coding) upper bound alpha with high probability, without specific distributional assumptions on the features and the responses. Universal the umbrella algorithm is, it demands an explicit minimum sample size requirement on class 0, which is often the more scarce class, such as in rare disease diagnosis applications. In this work, we employ the parametric linear discriminant analysis (LDA) model and propose a new parametric thresholding algorithm, which does not need the minimum sample size requirements on class 0 observations and thus is suitable for small sample applications such as rare disease diagnosis. Leveraging both the existing nonparametric and the newly proposed parametric thresholding rules, we propose four LDA-based NP classifiers, for both low- and high-dimensional settings. On the theoretical front, we prove NP oracle inequalities for one proposed classifier, where the rate for excess type II error benefits from the explicit parametric model assumption. Furthermore, as NP classifiers involve a sample splitting step of class 0 observations, we construct a new adaptive sample splitting scheme that can be applied universally to NP classifiers, and this adaptive strategy reduces the type II error of these classifiers. The proposed NP classifiers are implemented in the R package nproc.

**Date Heure/Time**: Le vendredi 13 mars 2020 - 16:00

**Lieu/Venue**: Pavillon André-Aisenstadt, Université de Montréal, salle 1175

**Conférencier/Speaker**: Almut Burchard , University of Toronto (ANNULÉ-CANCELLED)

**Titre/Title**: Optimal shapes arising from pair interactions

**Resume/Abstract**:

In many physical and social situations, pair interactions determine how a large group of particles or individuals arranges itself in space under constraints on the overall mass, density, and geometry. Typical examples are capacitor problems (where the interaction is purely repulsive), and flocking (where the interaction tends to be attractive at large distances and repulsive as individuals get too close). Mathematically, this leads to non-local shape optimization problems, where a density interacts with itself by a pair potential. Under what conditions is there aggregation, and when do individuals disperse? Is the optimal shape always round? Can multiple flocks co-exist? I will discuss some toy models, symmetrization techniques, recent results, and open questions.