Quebec Mathematical Sciences Colloquium

Quebec Mathematical Sciences Colloquium

Organized by the CRM in collaboration with the Institut des sciences mathématiques (ISM), the Colloque des sciences mathématiques du Québec offers a forum for mathematicians of great reputation, who are invited to give lectures of current and general interest, and accessible to the entire Quebec mathematical community. The tradition is that these lectures are as qualitative and non-technical as possible in order to be accessible to general graduate students in mathematics and statistics.

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Scientific Activities

November 13, 2020 from 15:30 to 16:30 (Montreal/Miami time) Zoom meeting

À venir / TBA

Colloquium presented by Tamara Broderick (Massachusetts Institute of Technology, USA)

November 27, 2020 from 15:00 to 16:00 (Montreal/Miami time) Zoom meeting

À venir / TBA

Colloquium presented by Frances Kirwan (University of Oxford)

Colloquia Schedule

To have access to the Zoom meeting link, please register to the Quebec Mathematical Sciences Colloquium. Registering once gives you access to every activity.

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Upcoming colloquia
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Start time Title Speaker
2020-11-13 15:30 À venir / TBA Tamara Broderick (Massachusetts Institute of Technology, USA)
2020-11-27 15:00 À venir / TBA Frances Kirwan (University of Oxford)

November 13, 2020 from 15:30 to 16:30 (Montreal/Miami time) Zoom meeting

À venir / TBA

Colloquium presented by Tamara Broderick (Massachusetts Institute of Technology, USA)

November 27, 2020 from 15:00 to 16:00 (Montreal/Miami time) Zoom meeting

À venir / TBA

Colloquium presented by Frances Kirwan (University of Oxford)

Past colloquia
Change display

Start time Title Speaker
2020-10-16 15:00 Trigonometric functions and modular symbols Nicolas Bergeron (École normale supérieure (Paris), France)
2020-10-09 15:00 Hodge Theory and Moduli Phillip Griffiths (Institute for Advanced Study, Princeton, USA)
2020-10-02 15:30 Data Science, Classification, Clustering and Three-Way Data Paul McNicholas (McMaster University, Canada)
2020-09-11 16:00 Machine Learning for Causual Inference Stefan Wager (Stanford University, USA)
2020-06-19 16:00 Quantitative approaches to understanding the immune response to SARS-CoV-2 infection Morgan Craig (Université de Montréal)
2020-04-17 16:00 Observable events and typical trajectories in finite and infinite dimensional dynamical systems Lai-Sang Young (New York University Courant)
2019-05-16 16:00 Introduction to birational classification theory in dimension three and higher Jungkay A. Chen (National Taiwan University)
2019-05-10 16:00 Quantum Jacobi forms and applications Amanda Folsom (Amherst College)
2019-05-03 16:00 The stochastic heat equation and KPZ in dimensions three and higher Lenya Ryzhik (Stanford University)
2019-04-26 16:00 Distinguishing finitely presented groups by their finite quotients Alan W. Reid (Rice University)
2019-04-12 16:00 Linking in torus bundles and Hecke L functions Nicolas Bergeron (École normale supérieure (Paris), France)
2019-03-29 16:00 Principal Bundles in Diophantine Geometry Minhyong Kim (University of Oxford)
2019-03-22 16:00 Flexibility in contact and symplectic geometry Emmy Murphy (Northwestern University)
2019-03-19 14:30 Special Colloquium : A constructive solution to Tarski’s circle squaring problem Andrew Marks (UCLA)
2019-03-15 16:00 Persistent homology as an invariant, rather than as an approximation Shmuel Weinberger (University of Chicago)
2018-11-02 16:00 The complexity of detecting cliques and cycles in random graphs
2018-09-28 16:00 A delay differential equation with a solution whose shortened segments are dense Hans-Otto Walther (Universität Giessen)
2018-09-21 16:00 Algebraic structures for topological summaries of data Ezra Miller (Duke University)
2018-05-04 16:00 Klein­-Gordon­-Maxwell­-Proca systems in the Riemannian setting Emmanuel Hebey (Université de Cergy-­Pontoise)
2018-04-13 16:00 Local-­global principles in number theory Eva Bayer (École Polytechnique Fédérale de Lausanne)
2018-02-23 16:00 Cluster theory of the coherent Satake category Sabin Cautis (University of British Columbia)
2018-02-16 16:00 Quantum n-­body problem: generalized Euler coordinates (from J-­L Lagrange to Figure Eight by Moore and Ter-­Martirosyan, then and today) Alexandre Turbiner (UNAM)
2018-02-16 15:30 The Law of Large Populations: The return of the long-­ignored N and how it can affect our 2020 vision Xiao-Li Meng (Harvard University)
2018-02-09 16:00 Persistence modules in symplectic topology Egor Shelukhin (Université de Montréal)
2018-01-12 16:00 What is quantum chaos Semyon Dyatlov (UC Berkeley / MIT)
2017-12-08 16:00 Primes with missing digits James Maynard (University of Oxford)
2017-11-24 15:30 150 years (and more) of data analysis in Canada David R. Bellhouse (Western University, London, Ontario)
2017-11-24 15:30 Complex analysis and 2D statistical physics Stanislav Smirnov (University of Geneva and Skolkovo Institute of Science and Technology)
2017-11-17 16:00 Recent progress on De Giorgi Conjecture Jun-Cheng Wei (UBC)
2017-10-27 16:00 Beneath the Surface: Geometry Processing at the Intrinsic/Extrinsic Interface Justin Solomon (M)
2017-10-13 16:00 Supercritical Wave Equations Avi Soffer (Rutgers University)
2017-09-29 16:00 The first field John H. Conway (Princeton University)
2017-09-15 16:00 Isometric embedding and quasi­-local type inequality Siyuan Lu (Rutgers University, Lauréat 2017 du Prix Carl Herz / 2017 Carl Herz Prize Winner)
2017-05-05 16:00 From the geometry of numbers to Arakelov geometry Gerard Freixas (Institut de Mathématiques de Jussieu)
2017-04-21 16:00 Introduction to the Energy Identity for Yang-­Mills Aaron Naber (Northwestern University)
2017-03-31 16:00 PDEs on non­-smooth domains Tatiana Toro (University of Washington)
2017-03-17 15:30 Inference in Dynamical Systems Sayan Mukherjee (Duke University)
2017-03-10 16:00 Probabilistic aspects of minimum spanning trees Louigi Addario-Berry (Université McGill)
2017-02-24 16:00 Spreading phenomena in integrodifference equations with overcompensatory growth function Frithjof Lutscher (Université d'Ottawa)
2017-02-10 16:00 Knot concordance Mark Powell (UQAM)
2017-01-20 16:00 The Birch­-Swinnerton Dyer Conjecture and counting elliptic curves of ranks 0 and 1 Christopher Skinner (Princeton University)
2016-12-02 16:00 Partial differential equations of mixed elliptic-­hyperbolic type in mechanics and geometry Gui-­Qiang G. Chen (University of Oxford)
2016-12-01 15:30 High­-dimensional changepoint estimation via sparse projection Richard Samworth (University of Cambridge)
2016-11-26 16:00 Around the Möbius function Maksym Radziwill (McGill University)
2016-11-04 16:00 The nonlinear stability of Minkowski space for self­-gravitating massive fields Philippe G. LeFloch (Université Pierre et Marie Curie, Paris 6)
2016-10-28 15:30 Efficient tests of covariate effects in two­-phase failure time studies Jerry Lawless (University of Waterloo)
2016-10-21 16:00 Integrable probability and the KPZ universality class Ivan Corwin (Columbia University)
2016-10-14 16:00 Rigorously verified computing for infinite dimensional nonlinear dynamics: a functional analytic approach Jean-Philippe Lessard (McGill University)
2016-09-30 16:00 Notions of simplicity in low­-dimensions Liam Watson (Université de Sherbrooke)
2016-09-16 16:00 Statistical Inference for fractional diffusion processes B.L.S. Prakasa Rao (CR Rao Advanced Institute, Hyderabad, India)
2016-09-16 16:00 Cubature, approximation, and isotropy in the hypercube Nick Trefethen (University of Oxford)

October 16, 2020 from 15:00 to 16:00 (Montreal/Miami time) Zoom meeting

Trigonometric functions and modular symbols

Colloquium presented by Nicolas Bergeron (École normale supérieure (Paris), France)

Chaire Aisenstadt Chair Conference

Thematic Semester: Number Theory - Cohomology in Arithmetic

Abstract:

In his fantastic book “Elliptic functions according to Eisenstein and Kronecker”, Weil writes:

“As Eisenstein shows, his method for constructing elliptic functions applies beautifully to the simpler case of the trigonometric functions. Moreover, this case provides […] the simplest proofs for a series of results, originally discovered by Euler.”

The results Weil alludes to are relations between product of trigonometric functions. I will first explain how these relations are quite surprisingly governed by relations between modular symbols (whose elementary theory I will sketch). I will then show how this story fits into a wider picture that relates the topological world of group homology of some linear groups to the algebraic world of trigonometric and elliptic functions. To conclude I will briefly describe a number theoretical application.

This is based on a work-in-progress with Pierre Charollois, Luis Garcia and Akshay Venkatesh.

October 9, 2020 from 15:00 to 16:00 (Montreal/Miami time) Zoom meeting

Hodge Theory and Moduli

Colloquium presented by Phillip Griffiths (Institute for Advanced Study, Princeton, USA)

The theory of moduli is an important and active area in algebraic geometry. For varieties of general type the existence of a moduli space with a canonical completion has been proved by Kollar/Shepard-Barron/Alexeev. Aside from the classical case of algebraic curves, very little is known about the structure of , especially it’s boundary. The period mapping from Hodge theory provides a tool for studying these issues.

In this talk, we will discuss some aspects of this topic with emphasis on I-surfaces, which provide one of the first examples where the theory has been worked out in some detail. Particular notice will me made of how the extension data in the limiting mixed Hodge structures that arise from singular surfaces on the boundary of moduli may be used to guide the desingularization of that boundary. 

Hodge Theory and Moduli

October 2, 2020 from 15:30 to 16:30 (Montreal/Miami time) Zoom meeting

Data Science, Classification, Clustering and Three-Way Data

Colloquium presented by Paul McNicholas (McMaster University, Canada)

Data science is discussed along with some historical perspective. Selected problems in classification are considered, either via specific datasets or general problem types. In each case, the problem is introduced before one or more potential solutions are discussed and applied. The problems discussed include data with outliers, longitudinal data, and three-way data. The proposed approaches are generally mixture model-based.

Organizers:
Erica E. M. Moodie (erica.moodie@mcgill.ca)
Yogendra P. Chaubey (yogen.chaubey@concordia.ca)

September 11, 2020 from 16:00 to 17:00 (Montreal/Miami time) Zoom meeting

Machine Learning for Causual Inference

Colloquium presented by Stefan Wager (Stanford University, USA)

Given advances in machine learning over the past decades, it is now possible to accurately solve difficult non-parametric prediction problems in a way that is routine and reproducible. In this talk, I’ll discuss how machine learning tools can be rigorously integrated into observational study analyses, and how they interact with classical statistical ideas around randomization, semiparametric modeling, double robustness, etc. I’ll also survey some recent advances in methods for treatment heterogeneity. When deployed carefully, machine learning enables us to develop causal estimators that reflect an observational study design more closely than basic linear regression based methods.

June 19, 2020 from 16:00 to 17:00 (Montreal/Miami time) Zoom meeting

Quantitative approaches to understanding the immune response to SARS-CoV-2 infection

Colloquium presented by Morgan Craig (Université de Montréal)

COVID-19 is typically characterized by a range of respiratory symptoms that, in severe cases, progress to acute respiratory distress syndrome (ARDS). These symptoms are also frequently accompanied by a range of inflammatory indications, particularly hyper-reactive and dysregulated inflammatory responses in the form of cytokine storms and severe immunopathology. Much remains to be uncovered about the mechanisms that lead to disparate outcomes in COVID-19. Here, quantitative approaches, especially mechanistic mathematical models, can be leveraged to improve our understanding of the immune response to SARS-CoV-2 infection.

Building upon our prior work modelling the production of innate immune cell subsets and the viral dynamics of HIV and oncolytic viruses, we are developing a quantitative framework to interrogate open questions about the innate and adaptive immune reaction in COVID-19. In this talk, I will outline our recent work modelling SARS-CoV-2 viral dynamics and the ensuing immune response at both the tissue and systemic levels. A portion of this work is done as part of an international and multidisciplinary coalition working to establish a comprehensive tissue simulator (physicell.org/covid19 [1]), which I will also discuss in more detail.

April 17, 2020 from 16:00 to 17:00 (Montreal/Miami time) Zoom meeting

Observable events and typical trajectories in finite and infinite dimensional dynamical systems

Colloquium presented by Lai-Sang Young (New York University Courant)

The terms "observable events" and "typical trajectories" in the title should really be between quotation marks, because what is typical and/or observable is a matter of interpretation. For dynamical systems on finite dimensional spaces, one often equates observable events with positive Lebesgue measure sets, and invariant distributions that reflect the large-time behaviors of positive Lebesgue measure sets of initial conditions (such as Liouville measure for Hamiltonian systems) are considered to be especially important. I will begin by introducing these concepts for general dynamical systems -- including those with attractors -- describing a simple dynamical picture that one might hope to be true. This picture does not always hold, unfortunately, but a small amount of random noise will bring it about. In the second part of my talk I will consider infinite dimensional systems such as semi-flows arising from dissipative evolutionary PDEs. I will discuss the extent to which the ideas above can be generalized to infinite dimensions, and propose a notion of "typical solutions".

May 16, 2019 from 16:00 to 18:00 (Montreal/Miami time) On location

Introduction to birational classification theory in dimension three and higher

Colloquium presented by Jungkay A. Chen (National Taiwan University)

One of the main themes of algebraic geometry is to classify algebraic varieties and to study various geometric properties of each of the interesting classes. Classical theories of curves and surfaces give a beautiful framework of classification theory. Recent developments provide more details in the case of dimension three. We are going to introduce the three-dimensional story and share some expectations for even higher dimensions.

Address

UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, room PK-5115

May 10, 2019 from 16:00 to 18:00 (Montreal/Miami time) On location

Quantum Jacobi forms and applications

Colloquium presented by Amanda Folsom (Amherst College)

Quantum modular forms were defined in 2010 by Zagier; they are somewhat analogous to ordinary modular forms, but they are defined on the rational numbers as opposed to the upper half complex plane, and have modified transformation properties. In 2016, Bringmann and the author defined the notion of a quantum Jacobi form, naturally marrying the concept of a quantum modular form with that of a Jacobi form (the theory of which was developed by Eichler and Zagier in the 1980s). We will discuss these intertwined topics, emphasizing recent developments and applications. In particular, we will discuss applications to combinatorics, topology (torus knots), and representation theory (VOAs).

Address

McGill University, Burnside Hall , 805 O., rue Sherbrooke, room 1104

May 3, 2019 from 16:00 to 18:00 (Montreal/Miami time) On location

The stochastic heat equation and KPZ in dimensions three and higher

Colloquium presented by Lenya Ryzhik (Stanford University)

The stochastic heat equation and the KPZ equation appear as the macroscopic limits for a large class of probabilistic models, and the study of KPZ, in particular, led to many fascinating developments in probability over the last decade or so, from the regularity structures to integrable probability. We will discuss a small group of recent results on these equations in simple settings, of the PDE flavour, that fall in line with what one may call naive expectations by an applied mathematician.

Address

McGill University, Burnside Hall , 805 O., rue Sherbrooke, room 1104

April 26, 2019 from 16:00 to 18:00 (Montreal/Miami time) On location

Distinguishing finitely presented groups by their finite quotients

Colloquium presented by Alan W. Reid (Rice University)

If G is a finitely generated group, let C(G) denote the set of finite quotients of G. This talk will survey work on the question of to what extent C(G) determines G up to isomorphism, culminating in a discussion of examples of Fuchsian and Kleinian groups that are determined by C(G) (amongst finitely generated residually finite groups).

Address

McGill University, Burnside Hall , 805 O., rue Sherbrooke, room 1104

April 12, 2019 from 16:00 to 18:00 (Montreal/Miami time) On location

Linking in torus bundles and Hecke L functions

Colloquium presented by Nicolas Bergeron (École normale supérieure (Paris), France)

Torus bundles over the circle are among the simplest and cutest examples of 3- dimensional manifolds. After presenting some of these examples, using in particular animations realized by Jos Leys, I will consider periodic orbits in these fiber bundles over the circle. We will see that their linking numbers --- that are rational numbers by definition --- can be computed as certain special values of Hecke L-functions. Properly generalized this viewpoint makes it possible to give new topological proof of now classical rationality or integrality theorems of Klingen-Siegel and Deligne-Ribet. It also leads to interesting new "arithmetic lifts" that I will briefly explain. All this is extracted from an on going joint work with Pierre Charollois, Luis Garcia and Akshay Venkatesh.

Address

McGill University, Burnside Hall , 805 O., rue Sherbrooke, room 1104

March 29, 2019 from 16:00 to 18:00 (Montreal/Miami time) On location

Principal Bundles in Diophantine Geometry

Colloquium presented by Minhyong Kim (University of Oxford)

Principal bundles and their moduli have been important in various aspects of physics and geometry for many decades. It is perhaps not so well-known that a substantial portion of the original motivation for studying them came from number theory, namely the study of Diophantine equations. I will describe a bit of this history and some recent developments.

Address

McGill University, Burnside Hall , 805 O., rue Sherbrooke, room 1104

March 22, 2019 from 16:00 to 18:00 (Montreal/Miami time) On location

Flexibility in contact and symplectic geometry

Colloquium presented by Emmy Murphy (Northwestern University)

We discuss a number of h-principle phenomena which were recently discovered in the field of contact and symplectic geometry. In generality, an h-principle is a method for constructing global solutions to underdetermined PDEs on manifolds by systematically localizing boundary conditions. In symplectic and contact geometry, these strategies typically are well suited for general constructions and partial classifications. Some of the results we discuss are the characterization of smooth manifolds admitting contact structures, high dimensional overtwistedness, the symplectic classification of flexibile Stein manifolds, and the construction of exotic Lagrangians in C^n.

Address

UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, room PK-5115

March 19, 2019 from 14:30 to 16:30 (Montreal/Miami time) On location

Special Colloquium : A constructive solution to Tarski’s circle squaring problem

Colloquium presented by Andrew Marks (UCLA)

In 1925, Tarski posed the problem of whether a disc in R^2 can be partitioned into finitely many pieces which can be rearranged by isometries to form a square of the same area. Unlike the Banach-Tarski paradox in R^3, it can be shown that two Lebesgue measurable sets in R^2 cannot be equidecomposed by isometries unless they have the same measure. Hence, the disk and square must necessarily be of the same area. In 1990, Laczkovich showed that Tarski’s circle squaring problem has a positive answer using the axiom of choice. We give a completely constructive solution to the problem and describe an explicit (Borel) way to equidecompose a circle and a square. This answers a question of Wagon. Our proof has three main ingredients. The first is work of Laczkovich in Diophantine approximation. The second is recent progress in a research program in descriptive set theory to understand how the complexity of a countable group is related to the complexity of the equivalence relations generated by its Borel actions. The third ingredient is ideas coming from the study of flows in networks. This is joint work with Spencer Unger.

Address

McGill University, Burnside Hall , 805 O., rue Sherbrooke, room 1104

March 15, 2019 from 16:00 to 18:00 (Montreal/Miami time) On location

Persistent homology as an invariant, rather than as an approximation

Colloquium presented by Shmuel Weinberger (University of Chicago)

Persistent homology is a very simple idea that was initially introduced as a way of understanding the underlying structure of an object from, perhaps noisy, samples of the object, and has been used as a tool in biology, material sciences, mapping and elsewhere. I will try to explain some of this, but perhaps also some more mathematical applications within geometric group theory. Then I'd like to pivot and study the part that traditionally has been thrown away, and show that this piece is relevant to approximation theory (a la Chebyshev), closed geodesics (a la Gromov), and to problems of quantitative topology (joint work with Ferry, Chambers, Dotter, and Manin).

Address

McGill University, Burnside Hall , 805, rue Sherbrooke O., salle/Room1104

November 2, 2018 from 16:00 to 17:00 (Montreal/Miami time)

The complexity of detecting cliques and cycles in random graphs

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 booleancircuits 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.

Address

CRM, Université de Montréal, Pavillon André-Aisenstadt, salle 1355

September 28, 2018 from 16:00 to 17:00 (Montreal/Miami time) On location

A delay differential equation with a solution whose shortened segments are dense

Colloquium presented by Hans-Otto Walther (Universität Giessen)

Simple-looking autonomous delay differential equations  with a real function and single time lag  can generate complicated (chaotic) solution behaviour, depending on the shape of . The same could be shown for equations with a variable, state-dependent delay , even for the linear case  with . Here the argument  of the {\it delay functional}  is the history of the solution  between  and t defined as the function  given by . 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  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  we construct a delay functional an infinite-dimensional subset of the space , so that the equation  has a solution whose {\it short segments} , , are dense in the space . This implies a new kind of complicated behaviour of the flowline . Reference: H. O. Walther, {\em A delay differential equation with a solution whose shortened segments are dense}.\\ J. Dynamics Dif. Eqs., to appear.

Address

McGill University, Burnside Hall, room 1104, 805 Sherbrooke W street

September 21, 2018 from 16:00 to 17:00 (Montreal/Miami time) On location

Algebraic structures for topological summaries of data

Colloquium presented by Ezra Miller (Duke University)

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.

Address

UQAM, Pavillon Président-Kennedy, 201 Président-Kennedy avenue, room PK-5115

May 4, 2018 from 16:00 to 18:00 (Montreal/Miami time) On location

Klein­-Gordon­-Maxwell­-Proca systems in the Riemannian setting

Colloquium presented by Emmanuel Hebey (Université de Cergy-­Pontoise)

We intend to give a general talk about Klein­-Gordon-­Maxwell-­Proca systems which we aim to be accessible to a broad audience. We will insist on the Proca contribution and then discuss the kind of results one can prove in the electromagneto static case of the equations.

Address

UQAM, pavillon Président-­Kennedy, 201, av. du Président­-Kennedy, room PK­5115

April 13, 2018 from 16:00 to 18:00 (Montreal/Miami time) On location

Local-­global principles in number theory

Colloquium presented by Eva Bayer (École Polytechnique Fédérale de Lausanne)

One of the classical tools of number theory is the so­called local­global principle, or Hasse principle, going back to Hasse's work in the 1920's. His first results concern quadratic forms, and norms of number fields. Over the years, many positive and negative results were proved, and there is now a huge number of results in this topic. This talk will present some old and new results, in particular in the continuation of Hasse's cyclic norm theorem. These have been obtained jointly with Parimala and Tingyu Lee.

Address

UQAM, pavillon Président-­Kennedy, 201, av. du Président-­Kennedy, room PK­5115

February 23, 2018 from 16:00 to 18:00 (Montreal/Miami time) On location

Cluster theory of the coherent Satake category

Colloquium presented by Sabin Cautis (University of British Columbia)

The affine Grassmannian, though a somewhat esoteric looking object at first sight, is a fundamental algebro­geometric construction lying at the heart of a series of ideas connecting number theory (and the Langlands program) to geometric representation theory, low dimensional topology and mathematical physics. Historically it is popular to study the category of constructible perverse sheaves on the affine Grassmannian. This leads to the *constructible* Satake category and the celebrated (geometric) Satake equivalence. More recently it has become apparent that it makes sense to also study the category of perverse *coherent* sheaves (the coherent Satake category). Motivated by certain ideas in mathematical physics this category is conjecturally governed by a cluster algebra structure. We will illustrate the geometry of the affine Grassmannian in an elementary way, discuss what we mean by a cluster algebra structure and then describe a solution to this conjecture in the case of general linear groups.

Address

UQAM, Pavillon Président-­Kennedy, 201, ave du Président-­Kennedy, room PK­5115

February 16, 2018 from 16:00 to 18:00 (Montreal/Miami time) On location

Quantum n-­body problem: generalized Euler coordinates (from J-­L Lagrange to Figure Eight by Moore and Ter-­Martirosyan, then and today)

Colloquium presented by Alexandre Turbiner (UNAM)

The potential of the n-­body problem, both classical and quantum, depends only on the relative (mutual) distances between bodies. By generalized Euler coordinates we mean relative distances and angles. Their advantage over Jacobi coordinates is emphasized. The NEW IDEA is to study trajectories in both classical, and eigenstates in quantum systems which depends on relative distances ALONE. We show how this study is equivalent to the study of (i) the motion of a particle (quantum or classical) in curved space of dimension n(n-­1)/2 or the study of (ii) the Euler-Arnold (quantum or classical) ­ - sl(n(n-­1)/2, R) algebra top. The curved space of (i) has a number of remarkable properties. In the 3­body case the {\it de­Quantization} of quantum Hamiltonian leads to a classical Hamiltonian which solves a ~250­-years old problem posed by Lagrange on 3­-body planar motion.

Address

CRM, Université de Montréal, Pavillon André­-Aisenstadt, room 6254

February 16, 2018 from 15:30 to 17:30 (Montreal/Miami time) On location

The Law of Large Populations: The return of the long-­ignored N and how it can affect our 2020 vision

Colloquium presented by Xiao-Li Meng (Harvard University)

For over a century now, we statisticians have successfully convinced ourselves and almost everyone else, that in statistical inference the size of the population N can be ignored, especially when it is large. Instead, we focused on the size of the sample, n, the key driving force for both the Law of Large Numbers and the Central Limit Theorem. We were thus taught that the statistical error (standard error) goes down with n typically at the rate of 1/√n. However, all these rely on the presumption that our data have perfect quality, in the sense of being equivalent to a probabilistic sample. A largely overlooked statistical identity, a potential counterpart to the Euler identity in mathematics, reveals a Law of Large Populations (LLP), a law that we should be all afraid of. That is, once we lose control over data quality, the systematic error (bias) in the usual estimators, relative to the benchmarking standard error from simple random sampling, goes up with N at the rate of √N. The coefficient in front of √N can be viewed as a data defect index, which is the simple Pearson correlation between the reporting/recording indicator and the value reported/recorded. Because of the multiplier√N, a seemingly tiny correlation, say, 0.005, can have detrimental effect on the quality of inference. Without understanding of this LLP, “big data” can do more harm than good because of the drastically inflated precision assessment hence a gross overconfidence, setting us up to be caught by surprise when the reality unfolds, as we all experienced during the 2016 US presidential election. Data from Cooperative Congressional Election Study (CCES, conducted by Stephen Ansolabehere, Douglas River and others, and analyzed by Shiro Kuriwaki), are used to estimate the data defect index for the 2016 US election, with the aim to gain a clearer vision for the 2020 election and beyond.

Address

McGill University, OTTO MAASS 217

February 9, 2018 from 16:00 to 18:00 (Montreal/Miami time) On location

Persistence modules in symplectic topology

Colloquium presented by Egor Shelukhin (Université de Montréal)

In order to resolve Vladimir Arnol'd's famous conjecture from the 1960's, giving lower bounds on the number of fixed points of Hamiltonian diffeomorphisms of a symplectic manifold, Andreas Floer has associated in the late 1980's a homology theory to the Hamiltonian action functional on the loop space of the manifold. It was known for a long time that this homology theory can be filtered by the values of the action functional, yielding information about metric invariants in symplectic topology (Hofer's metric, for example). We discuss a recent marriage between the filtered version of Floer theory and persistent homology, a new field of mathematics that has its origins in data analysis, providing examples of new ensuing results.

Address

UQAM, Pavillon Président-­Kennedy, 201, ave du Président-­Kennedy, room PK­5115

January 12, 2018 from 16:00 to 18:00 (Montreal/Miami time) On location

What is quantum chaos

Colloquium presented by Semyon Dyatlov (UC Berkeley / MIT)

Where do eigenfunctions of the Laplacian concentrate as eigenvalues go to infinity? Do they equidistribute or do they concentrate in an uneven way? It turns out that the answer depends on the nature of the geodesic flow. I will discuss various results in the case when the flow is chaotic: the Quantum Ergodicity theorem of Shnirelman, Colin de Verdière, and Zelditch, the Quantum Unique Ergodicity conjecture of Rudnick-­Sarnak, the progress on it by Lindenstrauss and Soundararajan, and the entropy bounds of Anantharaman­-Nonnenmacher. I will conclude with a recent lower bound on the mass of eigenfunctions obtained with Jin. It relies on a new tool called "fractal uncertainty principle" developed in the works with Bourgain and Zahl.

Address

CRM, Université de Montréal, Pavillon André-­Aisenstadt, room 6254

December 8, 2017 from 16:00 to 16:00 (Montreal/Miami time) On location

Primes with missing digits

Colloquium presented by James Maynard (University of Oxford)

Many famous open questions about primes can be interpreted as questions about the digits of primes in a given base. We will talk about recent work showing there are infinitely many primes with no 7 in their decimal expansion. (And similarly with 7 replaced by any other digit.) This shows the existence of primes in a 'thin' set of numbers (sets which contain at most X^{1­c} elements less than X) which is typically very difficult. The proof relies on a fun mixture of tools including Fourier analysis, Markov chains, Diophantine approximation, combinatorial geometry as well as tools from analytic number theory

Address

UQAM, Pavillon Président-­Kennedy, 201, ave du Président­-Kennedy, room PK­5115

November 24, 2017 from 15:30 to 17:30 (Montreal/Miami time) On location

150 years (and more) of data analysis in Canada

Colloquium presented by David R. Bellhouse (Western University, London, Ontario)

As Canada celebrates its 150th anniversary, it may be good to reflect on the past and future of data analysis and statistics in this country. In this talk, I will review the Victorian Statistics Movement and its effect in Canada, data analysis by a Montréal physician in the 1850s, a controversy over data analysis in the 1850s and 60s centred in Montréal, John A. MacDonald’s use of statistics, the Canadian insurance industry and the use of statistics, the beginning of mathematical statistics in Canada, the Fisherian revolution, the influence of Fisher, Neyman and Pearson, the computer revolution, and the emergence of data science.

Address

Université McGill, Leacock Building, room LEA 232

November 24, 2017 from 15:30 to 17:30 (Montreal/Miami time) On location

Complex analysis and 2D statistical physics

Colloquium presented by Stanislav Smirnov (University of Geneva and Skolkovo Institute of Science and Technology)

Over the last decades, there was much progress in understanding 2D lattice models of critical phenomena. It started with several theories, developed by physicists. Most notably, Conformal Field Theory led to spectacular predictions for 2D lattice models: e.g., critical percolation cluster a.s. has Hausdorff dimension $91/48$, while the number of selfavoiding length $N$ walks on the hexagonal lattice grows like $(\sqrt{2+\sqrt{2}})^N N^{11/32}$. While the algebraic framework of CFT is rather solid, rigorous arguments relating it to lattice models were lacking. More recently, mathematical approaches were developed, allowing not only for rigorous proofs of many such results, but also for new physical intuition. We will discuss some of the applications of complex analysis to the study of 2D lattice models.

Address

CRM, Université de Montréal, Pavillon André-­Aisenstadt, room 6254

November 17, 2017 from 16:00 to 18:00 (Montreal/Miami time) On location

Recent progress on De Giorgi Conjecture

Colloquium presented by Jun-Cheng Wei (UBC)

Classifying solutions to nonlinear partial differential equations are fundamental research in PDEs. In this talk, I will report recent progress made in classifying some elementary PDEs, starting with the De Giorgi Conjecture (1978). I will discuss the classification of global minimizers and finite Morse index solutions, relation with minimal surfaces and Toda integrable systems, as well as recent exciting developments in fractional De Giorgi Conjecture.

Address

UQAM, Pavillon Président­-Kennedy, 201, ave du Président­-Kennedy, room PK­5115

October 27, 2017 from 16:00 to 18:00 (Montreal/Miami time) On location

Beneath the Surface: Geometry Processing at the Intrinsic/Extrinsic Interface

Colloquium presented by Justin Solomon (M)

Algorithms for analyzing 3D surfaces find application in diverse fields from computer animation to medical imaging, manufacturing, and robotics. Reflecting a bias dating back to the early development of differential geometry, a disproportionate fraction of these algorithms focuses on discovering intrinsic shape properties, or those measurable along a surface without considering the surrounding space. This talk will summarize techniques to overcome this bias by developing a geometry processing pipeline that treats intrinsic and extrinsic geometry democratically. We describe theoretically­justified, stable algorithms that can characterize extrinsic shape from surface representations. In particular, we will show two strategies for computational extrinsic geometry. In our first approach, we will show how the discrete Laplace­Beltrami operator of a triangulated surface accompanied with the same operator for its offset determines the surface embedding up to rigid motion. In the second, we will treat a surface as the boundary of a volume rather than as a thin shell, using the Steklov (Dirichlet­to­Neumann) eigenproblem as the basis for developing volumetric spectral shape analysis algorithms without discretizing the interior.

Address

UdeM, Pavillon André-­Aisenstadt, room 6254

October 13, 2017 from 16:00 to 18:00 (Montreal/Miami time) On location

Supercritical Wave Equations

Colloquium presented by Avi Soffer (Rutgers University)

I will review the problem of Global existence for dispersive equations, in particular, supercritical equations. These equations who play a fundamental role in science, have been , and remain a major challenge in the field of Partial Differential Equations. They come in various forms, derived from Geometry, General Relativity, Fluid Dynamics, Field Theory. I present a new approach to classify the asymptotic behavior of wave equations, supercritical and others, and construct global solutions with large initial data. I will then describe current extensions to Nonlinear Schroedinger Equations.

Address

UdeM, Pavillon André-­Aisenstadt, room 6254

September 29, 2017 from 16:00 to 18:00 (Montreal/Miami time) On location

The first field

Colloquium presented by John H. Conway (Princeton University)

The “first field” is obtained by making the entries in its addition and multiplication tables be the smallest possibilities. It is really an interesting field that contains the integers, but with new addition and multiplication tables. For example, 2 x 2 = 3, 5 x 7 = 13, ... It extends to the infinite ordinals and the first infinite ordinal is the cube root of 2!

Address

UdeM, Pavillon André-­Aisenstadt, room 1140

September 15, 2017 from 16:00 to 18:00 (Montreal/Miami time) On location

Isometric embedding and quasi­-local type inequality

Colloquium presented by Siyuan Lu (Rutgers University, Lauréat 2017 du Prix Carl Herz / 2017 Carl Herz Prize Winner)

In this talk, we will first review the classic Weyl's embedding problem and its application in quasi­local mass. We will then discuss some recent progress on Weyl's embedding problem in general Riemannian manifold. Assuming isometric embedding into Schwarzschild manifold, we will further establish a quasi­local type inequality. This talk is based on works joint with Pengfei Guan and Pengzi Miao.

Address

UQAM, Pavillon Président-­Kennedy, 201, ave du Président-­Kennedy, room PK­5115

May 5, 2017 from 16:00 to 16:00 (Montreal/Miami time) On location

From the geometry of numbers to Arakelov geometry

Colloquium presented by Gerard Freixas (Institut de Mathématiques de Jussieu)

Arakelov geometry is a modern formalism that extends in various directions the geometry of numbers founded by Minkowski in the nineteenth century. The objects of study are arithmetic varieties, namely complex varieties that can be defined by polynomial equations with integer coefficients. The theory exploits the interplay between algebraic geometry and number theory and complex analysis and differential geometry. Recently, the formalism found beautiful and important applications to the so­called Kudla programme and the Colmez conjecture. In the talk, I will first introduce elementary facts in Minkowski's geometry of numbers. This will provide a motivation for the sequel, where I will give my own view of Arakelov geometry, by focusing on toy (but non­trivial) examples of one of the central theorems in the theory, the arithmetic Riemann­Roch theorem mainly due to Bismut, Gillet and Soulé, and generalizations. I hope there will be ingredients to satisfy different tastes, for instance modular forms (arithmetic aspect), analytic torsion (analytic aspect) and Selberg zeta functions (arithmetic, analytic and dynamic aspects).

Address

UQAM, Pavillon Président­-Kennedy, 201, ave du Président-­Kennedy, room PK­5115

April 21, 2017 from 16:00 to 16:00 (Montreal/Miami time) On location

Introduction to the Energy Identity for Yang-­Mills

Colloquium presented by Aaron Naber (Northwestern University)

In this talk we give an introduction to the analysis of the Yang­Mills equation in higher dimensions. In particular, when studying sequences of solutions we will study the manner in which blow up can occur, and how this blow up may be understood through the classical notions of the defect measure and bubbles. The energy identity is an explicit conjectural relationship, known to be true in dimension four, relating the energy density of the defect measure at a point to the bubbles which occur at that point, and we will give a brief overview of the recent proof of this result for general stationary Yang Mills in higher dimensions. The work is joint with Daniele Valtorta.

Address

UQAM, Pavillon Président­-Kennedy, 201, ave du Président­-Kennedy, room PK­5115

March 31, 2017 from 16:00 to 18:00 (Montreal/Miami time) On location

PDEs on non­-smooth domains

Colloquium presented by Tatiana Toro (University of Washington)

In these lecture we will discuss the relationship between the boundary regularity of the solutions to elliptic second order divergence form partial differential equations and the geometry of the boundary of the domain where they are defined. While in the smooth setting tools from classical PDEs are used to address this question, in the nonsmooth setting techniques from harmonic analysis and geometric measure theory are needed to tackle the problem. The goal is to present an overview of the recent developments in this very active area of research.

Address

UQAM, Pavillon Président­-Kennedy, 201, ave du Président­-Kennedy, room PK­5115

March 17, 2017 from 15:30 to 17:30 (Montreal/Miami time) On location

Inference in Dynamical Systems

Colloquium presented by Sayan Mukherjee (Duke University)

We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Furthermore, we show how some well­studied properties of dynamical systems imply the general statistical properties related to maximum likelihood estimation. Finally, we exhibit classical families of dynamical systems for which maximum likelihood estimation is consistent. Examples include shifts of finite type with Gibbs measures and Axiom A attractors with SRB measures. We also relate Bayesian inference to the thermodynamic formalism in tracking dynamical systems.

Address

McGill University, Burnside Hall, 805 Sherbrooke Ouest, room 1205

March 10, 2017 from 16:00 to 18:00 (Montreal/Miami time) On location

Probabilistic aspects of minimum spanning trees

Colloquium presented by Louigi Addario-Berry (Université McGill)

One of the most dynamic areas of probability theory is the study of the behaviour of discrete optimization problems on random inputs. My talk will focus on the probabilistic analysis of one of the first and foundational combinatorial optimization problems: the minimum spanning tree problem. The structure of a random minimum spanning tree (MST) of a graph G turns out to be intimately linked to the behaviour of critical and near­critical percolation on G. I will describe this connection, and present some results on the structure, scaling limits, and volume growth of random MSTs. It turns out that, on high­dimensional graphs, random minimum spanning trees are expected to be threedimensional when viewed intrinsically, and six­dimensional when viewed as embedded objects. Based on joint works with Nicolas Broutin, Christina Goldschmidt, Simon Griffiths, Ross Kang, Gregory Miermont, Bruce Reed, Sanchayan Sen.

Address

CRM, Université de Montréal, Pavillon André-­Aisenstadt, 2920 Chemin de la Tour, room 6254

February 24, 2017 from 16:00 to 18:00 (Montreal/Miami time) On location

Spreading phenomena in integrodifference equations with overcompensatory growth function

Colloquium presented by Frithjof Lutscher (Université d'Ottawa)

The globally observed phenomenon of the spread of invasive biological species with all its sometimes detrimental effects on native ecosystems has spurred intense mathematical research and modelling efforts into corresponding phenomena of spreading speeds and travelling waves. The standard modelling framework for such processes is based on reaction­ diffusion equations, but several aspects of an invasion can only be appropriately described by a discrete­time analogues, called integrodifference equations. The theory of spreading speeds and travelling waves in such integrodifference equations is well established for the "mono­stable" case, i.e. when the non­spatial dynamics show a globally stable positive steady state. When the positive state of the non­spatial dynamics is not stable, as is the case with the famous discrete logistic equation, it is unclear how the corresponding spatial spread profile evolves and at what speed. Previous simulations seemed to reveal a travelling profile in the form of a two­cycle, with or without spatial oscillations. The existence of a travelling wave solution has been proven, but its shape and stability remain unclear. In this talk, I will show simulations that suggest that there are several travelling profiles at different speeds. I will establish corresponding generalizations of the concept of a spreading speed and prove the existence of such speeds and travelling waves in the second­ iterate operator. I conjecture that rather than a travelling two­cycle for the next­generation operator, one observes a pair of stacked fronts for the second­iterate operator. I will relate the observations to the phenomenon of dynamic stabilization.

Address

CRM, Université de Montréal, Pavillon André-­Aisenstadt, 2920 Chemin de la Tour, room 6254

February 10, 2017 from 16:00 to 18:00 (Montreal/Miami time) On location

Knot concordance

Colloquium presented by Mark Powell (UQAM)

I will introduce the knot concordance group, give a survey of our current understanding of it and discuss some relationships with the topology of 4-­manifolds.

Address

UQAM, Pavillon Président­-Kennedy, 201, ave du Président­-Kennedy, room PK­5115

January 20, 2017 from 16:00 to 18:00 (Montreal/Miami time) On location

The Birch­-Swinnerton Dyer Conjecture and counting elliptic curves of ranks 0 and 1

Colloquium presented by Christopher Skinner (Princeton University)

This colloquium talk will begin with an introduction to the Birch­­-Swinnerton­-Dyer conjecture for elliptic curves -- just curves defined by the equations y^2=x^3+Ax+B -- and then describe recent advances that allow us to prove that lots of elliptic curves have rank zero or one.

Address

UQAM, Pavillon Président-­Kennedy, 201, ave du Président-­Kennedy, room PK­5115

December 2, 2016 from 16:00 to 18:00 (Montreal/Miami time) On location

Partial differential equations of mixed elliptic-­hyperbolic type in mechanics and geometry

Colloquium presented by Gui-­Qiang G. Chen (University of Oxford)

As is well­-known, two of the basic types of linear partial differential equations (PDEs) are hyperbolic PDEs and elliptic PDEs, following the classification for linear PDEs first proposed by Jacques Hadamard in the 1920s; and linear theories of PDEs of these two types have been well established, respectively. On the other hand, many nonlinear PDEs arising in mechanics, geometry, and other areas naturally are of mixed elliptic­hyperbolic type. The solution of some longstanding fundamental problems in these areas greatly requires a deep understanding of such nonlinear PDEs of mixed type. Important examples include shock reflection­-diffraction problems in fluid mechanics (the Euler equations) and isometric embedding problems in differential geometry (the Gauss-­Codazzi­Ricci equations), among many others. In this talk we will present natural connections of nonlinear PDEs of mixed elliptic­-hyperbolic type with these longstanding problems and will then discuss some recent developments in the analysis of these nonlinear PDEs through the examples with emphasis on developing and identifying mathematical approaches, ideas, and techniques for dealing with the mixed­-type problems. Further trends, perspectives, and open problems in this direction will also be addressed.

Address

UQAM, Pavillon Président-­Kennedy, 201, ave du Président­-Kennedy, room PK­5115

December 1, 2016 from 15:30 to 17:30 (Montreal/Miami time) On location

High­-dimensional changepoint estimation via sparse projection

Colloquium presented by Richard Samworth (University of Cambridge)

Changepoints are a very common feature of Big Data that arrive in the form of a data stream. We study highdimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the coordinates. The challenge is to borrow strength across the coordinates in order to detect smaller changes than could be observed in any individual component series. We propose a two­stage procedure called 'inspect' for estimation of the changepoints: first, we argue that a good projection direction can be obtained as the leading left singular vector of the matrix that solves a convex optimisation problem derived from the CUSUM transformation of the time series. We then apply an existing univariate changepoint detection algorithm to the projected series. Our theory provides strong guarantees on both the number of estimated changepoints and the rates of convergence of their locations, and our numerical studies validate its highly competitive empirical performance for a wide range of data generating mechanisms.

Address

Room 1205, Burnside Hall, 805 Sherbrooke West

November 26, 2016 from 16:00 to 18:00 (Montreal/Miami time) On location

Around the Möbius function

Colloquium presented by Maksym Radziwill (McGill University)

The Moebius function plays a central role in number theory; both the prime number theorem and the Riemann Hypothesis are naturally formulated in terms of the amount of cancellations one gets when summing the Moebius function. In recent joint work with K. Matomaki the speaker showed that the sum of the Moebius function exhibits cancellations in "almost all intervals'' of increasing length. This goes beyond what was previously known conditionally on the Riemann Hypothesis. The result holds in fact in greater generality. Exploiting this generality one can show that between a fixed number of consecutive squares there is always an integer composed of only "small'' prime factors. This is related to the running time of Lenstra's factoring algorithm. I will also discuss some further developments : the work of Tao on correlations between consecutive values of Chowla, and his application of this result to the resolution of the Erdos discrepancy problem.

Address

UQAM, Pavillon Président­-Kennedy, 201, ave du Président­-Kennedy, room PK­5115

November 4, 2016 from 16:00 to 18:00 (Montreal/Miami time) On location

The nonlinear stability of Minkowski space for self­-gravitating massive fields

Colloquium presented by Philippe G. LeFloch (Université Pierre et Marie Curie, Paris 6)

will review results on the global evolution of self­gravitating massive matter in the context of Einstein's theory as well as the f(R)­theory of gravity. In collaboration with Yue Ma (Xian), I have investigated the global existence problem for the Einstein equations coupled with a Klein­Gordon equation describing the evolution of a massive scalar field. Our main theorem establishes the global nonlinear stability of Minkowski spacetime upon small perturbations of the metric and the matter field. Recall that the fully geometric proof by Christodoulou and Klainerman in 1993, as well as the proof in wave gauge by Lindblad and Rodnianski in 2010, both apply to vacuum spacetimes and massless fields only. Our new technique of proof, which we refer to as the Hyperboloidal Foliation Method, does not use Minkowski's scaling field and is based on a foliation of the spacetime by asymptotically hyperboloidal spacelike hypersurfaces, on sharp estimates for wave and Klein­Gordon equations, and on an analysis of the quasi­null hyperboloidal structure (as we call it) of the Einstein equations in wave gauge.

Address

CRM, Pavillon André-­Aisenstadt, 2920 chemin de la tour, room 6254

October 28, 2016 from 15:30 to 17:30 (Montreal/Miami time) On location

Efficient tests of covariate effects in two­-phase failure time studies

Colloquium presented by Jerry Lawless (University of Waterloo)

Two-­phase studies are frequently used when observations on certain variables are expensive or difficult to obtain. One such situation is when a cohort exists for which certain variables have been measured (phase 1 data); then, a subsample of individuals is selected, and additional data are collected on them (phase 2). Efficiency for tests and estimators can be increased by basing the selection of phase 2 individuals on data collected at phase 1. For example, in large cohorts, expensive genomic measurements are often collected at phase 2, with oversampling of persons with “extreme” phenotypic responses. A second example is case­cohort or nested case­control studies involving times to rare events, where phase 2 oversamples persons who have experienced the event by a certain time. In this talk I will describe two­phase studies on failure times, present efficient methods for testing covariate effects. Some extensions to more complex outcomes and areas needing further development will be discussed.

Address

Room 1205, Burnside Hall, 805 Sherbrooke West

October 21, 2016 from 16:00 to 16:00 (Montreal/Miami time) On location

Integrable probability and the KPZ universality class

Colloquium presented by Ivan Corwin (Columbia University)

I will explain how certain integrable structures give rise to meaningful probabilistic systems and methods to analyze them. Asymptotics reveal universal phenomena, such as the Kardar­Parisi­Zhang universality class. No prior knowledge will be assumed.

Address

CRM, Pavillon André-­Aisenstadt, 2920 chemin de la tour, room 6254

October 14, 2016 from 16:00 to 18:00 (Montreal/Miami time) On location

Rigorously verified computing for infinite dimensional nonlinear dynamics: a functional analytic approach

Colloquium presented by Jean-Philippe Lessard (McGill University)

Studying and proving existence of solutions of nonlinear dynamical systems using standard analytic techniques is a challenging problem. In particular, this problem is even more challenging for partial differential equations, variational problems or functional delay equations which are naturally defined on infinite dimensional function spaces. The goal of this talk is to present rigorous numerical technique relying on functional analytic and topological tools to prove existence of steady states, time periodic solutions, traveling waves and connecting orbits for the above mentioned dynamical systems. We will spend some time identifying difficulties of the proposed approach as well as time to identify future directions of research.

Address

CRM, Pavillon André­-Aisenstadt, 2920 chemin de la tour, room 6254

September 30, 2016 from 16:00 to 18:00 (Montreal/Miami time) On location

Notions of simplicity in low­-dimensions

Colloquium presented by Liam Watson (Université de Sherbrooke)

Various auxiliary structures arise naturally in low­dimensions. I will discuss three of these: left­orders on the fundamental group, taut foliations on three­manifolds, and non­trivial Floer homological invariants. Perhaps surprisingly, for (closed, connected, orientable, irreducible) three­manifolds, it has been conjectured that the existence of any one of these structures implies the others. I will describe what is currently known about this conjectural relationship, as well as some of the machinery — particularly in Heegaard Floer theory — that has been developed in pursuit of the conjecture.

Address

UQAM, Pavillon Président-­Kennedy, 201, ave du Président-­Kennedy, room PK­5115

September 16, 2016 from 16:00 to 18:00 (Montreal/Miami time) On location

Statistical Inference for fractional diffusion processes

Colloquium presented by B.L.S. Prakasa Rao (CR Rao Advanced Institute, Hyderabad, India)

There are some time series which exhibit long­range dependence as noticed by Hurst in his investigations of river water levels along Nile river. Long­range dependence is connected with the concept of self­similarity in that increments of a self­similar process with stationary increments exhibit long­range dependence under some conditions. Fractional Brownian motion is an example of such a process. We discuss statistical inference for stochastic processes modeled by stochastic differential equations driven by a fractional Brownian motion. These processes are termed as fractional diffusion processes. Since fractional Brownian motion is not a semimartingale, it is not possible to extend the notion of a stochastic integral with respect to a fractional Brownian motion following the ideas of Ito integration. There are other methods of extending integration with respect to a fractional Brownian motion. Suppose a complete path of a fractional diffusion process is observed over a finite time interval. We will present some results on inference problems for such processes.

Address

Université Concordia, Library Building, 1400 de Maisonneuve O., room LB­921.04

September 16, 2016 from 16:00 to 18:00 (Montreal/Miami time) On location

Cubature, approximation, and isotropy in the hypercube

Colloquium presented by Nick Trefethen (University of Oxford)

The hypercube is the standard domain for computation in higher dimensions. We describe two respects in which the anisotropy of this domain has practical consequences. The first is a matter well known to experts (and to Chebfun users): the importance of axis­alignment in low­rank compression of multivariate functions. Rotating a function by a few degrees in two or more dimensions may change its numerical rank completely. The second is new. The standard notion of degree of a multivariate polynomial, total degree, is isotropic – invariant under rotation. The hypercube, however, is highly anisotropic. We present a theorem showing that as a consequence, the convergence rate of multivariate polynomial approximations in a hypercube is determined not by the total degree but by the {\em Euclidean degree,} defined in terms of not the 1­norm but the 2­norm of the exponent vector $\bf k$ of a monomial $x_1^{k_1}\cdots x_s^{k_s}$. The consequences, which relate to established ideas of cubature and approximation going back to James Clark Maxwell, are exponentially pronounced as the dimension of the hypercube increases. The talk will include numerical demonstrations.

Address

UQAM, Pavillon Président­-Kennedy, 201, ave du Président-Kennedy, room PK­5115
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Andrew Granville

Université de Montréal

Biography

Andrew Granville has been a Canadian Research Chair in number theory at the University of Montreal since 2002. He works primarily in analytic number theory, though has also published in additive combinatorics, algebraic number theory, graph theory, harmonic analysis and theoretical computer science. He has authored about 180 papers and 3 books including the graphic novel "Prime Suspects: The anatomy of integers and permutations" Princeton University press, 2019. He has won various prizes including the Jeffrey-Williams prize of the CMS, the Chauvenet prize of the MAA and the Presidential Faculty Fellowship from the NSF. He has graduated 29 PhD students so far, including 5 in 2020, and is an FRSC as well as a member of the Academia Europaea.

Jacques Hurtubise

Professor

McGill University

Biography

Jacques Hurtubise is a member of the Department of Mathematics and Statistics at McGill University, where he is currently the Chair. After obtaining his D.Phil. in 1982 from Oxford University, he spent five years at the Université du Québec à Montréal, before moving to McGill in 1988. In 1996-2003 he served as Deputy Director, then Director, of the Centre de Recherches Mathématiques. His research touches on various aspects of algebraic and differential geometry, in particular those linking in to mathematical physics.

Jessica Lin

McGill University

Biography

Jessica Lin is an Assistant Professor at McGill University and a Canada Research Chair in Partial Differential Equations and Probability (Tier 2). After completing her undergraduate degree at NYU/Courant Institute, she went on to pursue her graduate studies the University of Chicago, supported by a National Science Foundation Graduate Research Fellowship and the Clare Boothe Luce Fellowship. She received her PhD in 2014 under the supervision of Takis Souganidis. Before coming to McGill, she completed a postdoctoral fellowship at the University of Wisconsin--Madison under the supervision of Timo Seppalainen and Andrej Zlatos. Her research is broadly concerned with the asymptotic behaviour of physical systems subject to randomness, which she approaches using a combination of methods from both PDEs and probability.

Biography

Erica E. M. Moodie obtained her MPhil in Epidemiology in 2001 from the University of Cambridge, and a PhD in Biostatistics in 2006 from the University of Washington, before joining McGill University where she is now a William Dawson Scholar and Associate Professor of Biostatistics. Her main research interests are in causal inference and longitudinal data with a focus on adaptive treatment strategies. She is an Elected Member of the International Statistical Institute, and an Associate Editor of Biometrics. She holds a Chercheur-Boursier senior career award from the Fonds de recherche du Québec-Santé. She is the recipient of the 2020 CRM-SSC Prize in Statistics.

She is working with a team led by Nicole Basta on public awareness of SARS-Cov-2 vaccine development, and with the Canadian Longitudinal Study on Aging to understand the interplay of frailty and SARS-CoV-2 infection among the elderly.

Archive

To access the archive of all the activities of the Colloque des sciences mathématiques du Québec, please use the link below.