Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Probability Seminar - Camille Male (Bordeaux)

Tuesday, April 10th, 2018

Time: 3:30-5:00 p.m.  Place: Jeffery Hall 319

Speaker: Camille Male (Bordeaux)

Title: An introduction to traffic independence

Abstract: 

The properties of the limiting non-commutative distribution of random matrices can be usually understood thanks to the symmetry of the model, e.g. Voiculescu's asymptotic free independence occurs for random matrices invariant in law by conjugation by unitary matrices. The study of random matrices invariant in law by conjugation by permutation matrices requires an extension of free probability, which motivated the speaker to introduce in 2011 the theory of traffics. A traffic is a non-commutative random variable in a space with more structure than a general non-commutative probability space, so that the notion of traffic distribution is richer than the notion of non-commutative distribution. It comes with a notion of independence which is able to encode the different notions of non-commutative independence.

The purpose of this task is to present the motivation of this theory and to play with the notion of traffic independence.

Free Probability and Random Matrices Seminar Webpage:

Department Colloquium - Amie Wilkinson (University of Chicago)

Amie Wilkinson, University of Chicago

Friday, April 6th, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Amie Wilkinson, University of Chicago

Title: Robust Mechanisms for Chaos

Abstract: What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics? In addressing this question, I will focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations." I will describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.

Amie Wilkinson (University of Chicago): Prof. Amie Wilkinson received her BA from Harvard and her Ph.D. from the University of California at Berkeley. After a post-doc at Harvard, she became a professor at North­ western University, where she stayed 13 years, before moving to the University of Chicago in 2012. Prof. Wilkinson is a leading researcher in ergodic theory and dynamical sys­ tems. Among other recognitions of her many achievements, she was an invited speaker at the International Congress of Mathematicians in 2010, was awarded the Satter Prize in Mathematics in 2011, and was elected a fellow of the AMS in 2014. Prof. Wilkinson has also been very active in public outreach, giving numerous public lectures, interviews, and recently publishing an article in the New York Times.

Fields Lecture Series - Amie Wilkinson (University of Chicago)

Amie Wilkinson, University of Chicago

Thursday, April 5th, 2018

Time: 5:30 p.m.  Place: Jeffery Hall 127

Speaker: Amie Wilkinson, University of Chicago

Title: The Mathematics of Deja Vu

Abstract: Dynamics is an area of mathematics concerned with the motion of spaces (" dynamical systems") over time. Dynamics has its roots in the late nineteenth century, when it was developed as a tool to understand physical phenomena, such as the motion of gas molecules in a box and planets around the sun. A simple and yet powerful concept in dynamics is that of recurrence. In everyday language, recurrence is the mathematical version of deja vu: a motion of a space is recurrent if, given enough time, it eventually returns to its original configuration (allowing for a small amount of error). In this talk, I will describe how mathematical results about recurrence can be used to answer surprisingly disparate questions, from the mixing and unmixing of two ideaI gases in a box, to deep properties of the prime numbers, to the discovery of exoplanets in nearby solar systems.

Amie Wilkinson (University of Chicago): Prof Wilkinson (University of Chicago) is a leading researcher in ergodic theory and dynamical systems. Among other recognitions of her many achievements, she was an invited speaker at the International Congress of Mathematicians in 2010, was awarded the Satter Prize in Mathematics in 2011, and was elected a fellow of the AMS in 2014. Prof Wilkinson has also been very active in public outreach, giving numerous public lectures, interviews, and recently publishing an article in the New York Times.

Number Theory - Neha Prabhu (Queen's University)

Wednesday, April 4th, 2018

Time: 2:15 p.m.  Place: Jeffery Hall 319

Speaker: Neha Prabhu (Queen's University)

Title: Moments of the error term in the Sato-Tate law for elliptic curves.

Abstract: The Sato-Tate theorem for elliptic curves was proved by L. Clozel, M. Harris, N. Shepherd-Barron and R. Taylor in a series of papers from 2008-2010. Since the Sato-Tate law is an asymptotic statement, one is naturally interested in studying the nature of the error terms. In this talk, I shall describe some results relating to moments of the error term when we consider averages over certain families of elliptic curves. This is joint work with Stephan Baier.

Probability Seminar - Pei-Lun Tseng (Queen's University)

Tuesday, April 3rd, 2018

Time: 3:30-5:00 p.m.  Place: Jeffery Hall 319

Speaker: Pei-Lun Tseng (Queen's University)

Title: Linearization trick of infinitesimal freeness II

Abstract:  Last week, we introduced how to find a linearization for a given selfadjoint polynomial and showed some properties of this linearization. We will continue our discussion this week and introduce the operator-valued Cauchy transform. Then, we will show the algorithm for finding the distribution of $P$ where $P$ is a selfadjoint polynomial with selfadjoint variables $X$ and $Y$. Based on this method, we will discuss how to extend this algorithm for finding infinitesimal distribution for $P$.

Free Probability and Random Matrices Seminar Webpage:

Math Club - Jamie Mingo (Queen's University)

Thursday, March 29th, 2018

Time: 5:30 p.m.  Place: Jeffery Hall 118

Speaker: Jamie Mingo (Queen's University)

Title: Paradoxical Probabilities.

Abstract: Since the early days of probability theory there have been paradoxical statements, usually the result of implicit assumptions. The best known example is the Monty Hall problem. In this talk I discuss several examples, in particular the "bigger number paradox".

Geometry & Representation - Mike Zabrocki (York University)

Wednesday, March 28th, 2018

Time: 3:30 p.m.  Place: Jeffery Hall 319

Speaker: Mike Zabrocki (York University)

Title: A Multiset Partition Algebra

Abstract:  Schur-Weyl duality is a statement about the relationship between the actions of the general linear group $Gl_n$ and the symmetric group $S_k$ when these groups act on $V_n^{\otimes k}$ (here $V_n$ is an $n$ dimensional vector space). If we consider the symmetric group $S_n$ as permutation matrices embedded in $Gl_n$, then the partition algebra $P_k(n)$ (introduced by Martin in the 1990's) is the algebra which commutes with the action of $S_n$.

In this talk I will explain how an investigation of characters of the symmetric group leads us to consider analogues of the RSK algorithm involving multiset tableaux. To explain the relationship of the combinatorics to representation theory we were led to the multiset partition algebra as an analogue of the partition algebra and the dimensions of the irreducible representations are the numbers of multiset tableaux.

This is joint work with Rosa Orellana of Dartmouth College.

Number Theory - Siddhi Pathak (Queen's University)

Wednesday, March 28th, 2018

Time: 2:15 p.m.  Place: Jeffery Hall 319

Speaker: Siddhi Pathak (Queen's University)

Title: On the primitivity of Dirichlet characters.

Abstract: A Dirichlet character modulo q is said to be imprimitive if it is induced from a lower level. A characterization of the primitivity of characters is the separability of the Gauss sum ( Fourier transform of $\chi$ ), i.e., $G_q(n, \bar{chi}) = \chi(n) G_q(1, \bar{ \chi } )$ for all n. In this talk, we discuss a paper of R. Daielda and N. Jones in which they introduce another way of extending primitive Dirichlet characters so that the above separability property holds even for imprimitive characters.

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