Mathematics, Science and Technology

Delocalization of Schrödinger eigenfunctions

  October 22018    16:00 - 16:50   MSA 3.520
  There will be drinks and snacks after the talk

Abstract. A hundred years ago, Einstein wondered about quantization conditions for classically ergodic systems. Although a mathematical description of the spectrum of Schrödinger operators associated to ergodic classical dynamics is still completely missing, a lot of progress has been made on the delocalization of the associated eigenfunctions.

Meet the speaker…  Nalini Anantharaman is Professor of Mathematics at the University of Strasbourg. She previously held professorships at the École Polytechnique and the Université Paris-Sud. She works in several areas including mathematical physics, dynamical systems and spectral theory. Her contributions to mathematics have been recognized by many prizes including the Henri Poincaré prize, the Grand Prix Jacques Herbrand, and a CNRS silver medal. In 2018, she was a plenary speaker at the International Congress of Mathematicians in Rio.

A hyperbolic manifold fibering over the circle (and a theorem of Ian Agol and Dani Wise)

  December 4 2018    16:30 - 17:20   MSA 3.520
  There will be drinks and snacks after the talk

Abstract. In 1979 Jorgensen surprised geometers by constructing a 3-dimensional hyperbolic manifold fibering over the circle. Thirty-three years later Agol, using deep works of Wise, settled positively a question raised by William Thurston by proving that in fact every hyperbolic 3-manifold has a finite cover that fibers over the circle. In this talk, following an idea of Thurston, I will first construct an explicit example of a 3-dimensional hyperbolic manifolds fibering over the circle. The construction is elementary and can be made completely visual. The presentation will consist of a succession of short films, made with Jos Leys. In commenting on these films, I will try to explain how some of the ideas behind this construction relate to some of the basic ideas of the breakthrough of Agol and Wise.

Meet the speaker… Nicolas Bergeron is Professor of Mathematics at Sorbonne Université. He previously held a CNRS position at École Normale Supérieure (Paris) and the Université Paris-Sud. He has made key contributions to the understanding of the topology and geometry of locally symmetric spaces, arithmetic groups, and their cohomology. He was awarded a CNRS bronze medal in 2007, and is member of Institut Universitaire de France.

Systems of points with Coulomb interactions

  January 22 2019    16:10 - 17:00   MSA 3.110
  There will be drinks and snacks after the talk

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.

Meet the speaker… Sylvia Serfaty is Professor of Mathematics at Université Pierre et Marie Curie and is Global distinguished Professor at the Courant Institute of Mathematical Sciences (New York University). She has made key contributions to the analysis of nonlinear Partial Differential Equations arising from physics. She was awarded the Henri Poincaré Prize in 2012, and is a member of the Institut Universitaire de France. In 2018, she was a plenary speaker at the International Congress of Mathematicians in Rio.

Variational sums in statistics and probability.

  February 26 2019    16:30 - 17:20   MSA 3.520
  There will be drinks and snacks after the talk

Abstract. Variations are a standard tool in analysis and integration theory. While they are often used to study path properties of a function or to compute the fractional dimension, they are also extremely important in statistics and probability. In this talk we will review some statistical theory for diffusion processes, which is heavily based upon the probabilistic analysis of the so called power variations and their extensions. We will highlight numerous estimating and testing procedures, which gained popularity in financial applications. We further demonstrate possible extensions of the asymptotic theory to fractional models.

Meet the speaker… Mark Podolskij is full professor in Mathematics at the university of Aarhus. He made seminal contributions to probabilistic limit theorems, statistical analysis of stochastic processes and random fields, econometrics and mathematical finance. He is the current Editor in Chief of “Bernoulli”, one of the most influential journals in the fields of Probability and Mathematical Statistics. In 2018, he was awarded an ERC consolidator grant, for research on “Statistical methods for high-dimensional diffusions”.

Consistent Choice

  March 12 2019    16:30 - 17:20   MSA 3.350
  There will be drinks and snacks after the talk

Abstract. Much of economic and political theory is based on the notion of choice. Consumers choose commodity bundles, firms choose production plans, governments choose public projects, and voters choose their representatives by means of elections, for example. A central hypothesis is that choices are rational in the sense that they are made with a purpose, and purposive choice is typically associated with a goodness relation: observed choices are rational if there is an at-least-as-good-as relation such that, according to this relation, the selected objects are best among those that are available. An immediate question is what coherence properties such a goodness relation should possess. This usually involves the exclusion of goodness cycles, and the standard condition is transitivity. Because transitivity can be considered very demanding (especially in group decisions), it is desirable to explore weaker conditions. One possibility is the use of a consistency property that rules out specific cycles but does so without requiring full transitivity. The presentation is focused on the use of consistency in individual and collective choice.

A relevant non exhaustive bibliography can be downloaded.

Meet the speaker… Walter Bossert is Professor of Economics at the University of Montreal. He previously held professorships at the University of Nottingham, the University of Waterloo, and the University of Karlsruhe. He has made key contributions to social choice theory, in particular in rational choice theory.

Mathematical interventions in democracy

  March 19 2019    16:30 - 17:20   MSA 3.110
  There will be drinks and snacks after the talk

Abstract. Most countries of the world are divided up into administrative units—regions, departments, cantons, states—and into electoral units, such as districts or Luxembourg's circonscriptions. In the U.S., the districts must be re-drawn at regular intervals, and the process is usually controlled by politicians. For instance Pennsylvania, with its 12.7 million people, needs a partition into 18 winner-take-all districts. The number of ways to do this is staggering, and the choices have a massive impact on democratic outcomes. I'll describe several years of work thinking about how geometry and computing can illuminate the dynamics of districting, at one point as a consultant for the governor of Pennsylvania.

Meet the speaker…  Moon Duchin, an American mathematician at Tufts University, works in geometric group theory and topology. She has also made significant contributions to the mathematics of redistricting and gerrymandering. She is a Fellow of the AMS, and received multiple awards for her research and contributions including a Guggenheim Fellowship in 2018.

Set Theory fifty years after Cohen

  May 14 2019    16:30 - 17:20   MSA 3.330
  There will be drinks and snacks after the talk

Abstract. We shall explain a few results of modern Set Theory, with a special emphasis on two topics:

• the Continuum Problem and the meaning of solving the question after the well known negative results of Goedel and Cohen, and
• Laver tables, which are explicit finite structures, some simple combinatorial properties of which have so far been proved only using (unprovable) large cardinal axioms, a very paradoxical situation.

The talk will be accessible to everyone, with no prerequisite other than basic definitions involving real numbers.

Meet the speaker… Patrick Dehornoy is Professor of Mathematics at the University of Caen. He previously held the position of scientific deputy director of the INSMI institute of the CNRS, and is a member of the Institut Universitaire de France. He has made key contributions in the investigation of braid groups, Garside monoids and extensions, and General Artin-Tits groups. He was awarded Langevin Prize by the French Academy of Sciences in 2005.

Tessellations of the plane and beyond

  April 23 2019    16:30 - 17:20   MSA 3.040
  There will be drinks and snacks after the talk

Abstract. Tessellations of the plane have been used since antiquity as decorative patterns. With the development of modern mathematics, periodic tilings of Rⁿ have been extensively studied in relation to crystallography; they include Euclidean tilings but also, more generally, tilings whose symmetry group consists of affine transformations. When the tiles are noncompact, the symmetry group may no longer be a group of translations up to finite index, and tilings with interesting nonsolvable symmetry groups have been constructed since the 1980s. We will discuss some of these developments, including recent joint work with J. Danciger and F. Guéritaud.

Meet the speaker…  Fanny Kassel is a CNRS researcher working at the Institute of Advanced Scientific Studies (IHÉS). Her research often focusses on the interplay between geometric structures and representations of discrete groups. Her contributions to mathematics have been lauded with prizes and recognition, including being an invited ICM speaker in Rio in 2018, a CNRS bronze medal and an ERC starting grant.

A stroll in the world of finitely generated groups

  December 17 2019    16:00 - 16:50   MSA 3.110

Abstract. A group is a mathematical object intrinsically linked with the notions of symmetry and transformation. Formally, it is a set equipped with a binary operation that combines any two elements to form a third element in such a way that four axioms are satisfied: closure, associativity, identity and invertibility. Groups that can be described using only finitely many elements are called finitely generated and will be the focus of this talk: I will give examples, show pictures to explain where some of them come from, what they may look like, and discuss a potential application in cryptography.

Meet the speaker…  Indira Chatterji is now a professor at the University of Nice after having held positions in Orléans, Ohio, Cornell and a PhD at the ETH in Zürich. She is an expert in Geometric group theory, has been recognized by numerous grants and awards and is an editor at several leading mathematics journals.

From Thurston's Corrugations to Smooth Fractals

  February 20 2020    16:30 - 17:20   MSA 3.110
  There will be drinks and snacks after the talk

Abstract. The Theory of Corrugations is developped in the 70's by Thurston to dispel the mysterious reputation of the Smale's theorem on sphere immersions. A famous corollary of this theorem states that it is possible to smoothly and continuously turn a sphere inside out without creating any crease. The Theory of Corrugations provides both a geometric insight and a general method to construct eversions. By the way, the method is used in the 90's to produce a computer-graphics animation of a sphere eversion. Meanwhile, it is realized that corrugations also appear in the heart of another celebrated result, the C¹ Nash embedding Theorem. This theorem considers isometric maps - i. e. maps that preserve the length of curves- with regularity C¹ and has numerous paradoxical corollaries. For instance, it is possible to achieve an isometric eversion of the sphere. The study of these C¹ isometric maps puts into light unusual objects halfway between fractals and ordinary surfaces: smooth fractals.

Meet the speaker…  Vincent Borrelli, from the University of Lyon, works on the interface of geometry, analysis and computational mathematics. Notable results include his work together with S. Jabrane, F. Lazarus et B. Thibert on explicit embeddings of flat tori in Euclidean space. He is also an active outreacher with many articles in popular science magazines and is actively engaged in widely communicating the beauty of mathematics.