Department of Mathematics and Statistics

Friday, October 19th, 2018

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

Speaker: Camille Horbez (CNRS – Universite Paris Sud)

Title: Mostow-type rigidity and normal subgroups of automorphisms of free groups.

Abstract: The talk is based on a recent joint work with Richard D. Wade. Let Out(Fn) be the outer automorphism group of a finitely generated free group. In 2007, Farb and Handel proved that when n is at least 4, every isomorphism between two finite-index subgroups of Out(Fn) extends to an inner automorphism of Out(Fn). This rigidity statement, asserting that Out(Fn) has no more symmetries than the obvious ones, can be viewed as an analogue of the Mostow rigidity theorem for lattices in Lie groups, or of a result of Ivanov for mapping class groups of surfaces. We recently gave a new proof of Farb and Handel's theorem, which enabled us to also understand the symmetries of some natural normal subgroups of Out(Fn). In my talk, I will emphasize the analogies between Out(Fn), arithmetic groups and mapping class groups, and will present some general ideas behind these rigidity phenomena.

Camille Horbez obtained his Ph.D in at the Universite de Rennes in 2014, and after a year at the University of Utah, he became a Charge de Recherches for the CNRS at the Universite de Paris Sud (Orsay). In 2017, Camille was selected to give a Cours Peccot, a semester long course given at the College de France by a mathematician less than 30 year old.

Thursday, October 18th, 2018

Time: 11:30 a.m - 12:20 p.m Place: Jeffery Hall 422

Speaker: Noriko Yui (Queen's University)

Title: Four-dimensional Galois representations arising from certain Calabi--Yau threefolds Part II

Abstract: We consider the (irreducible) four-dimensional Galois representations arising from certain Calabi--Yau threefolds over ${\bf{Q}}$ with all the Hodge numbers of the third cohomology groups equal to $1$. There are many examples of (families) of such Calabi--Yau threefolds. The modularity/automorphy of such Calabi--Yau threefolds will be the main topic of discussion. There are two venues to be considered. In one venue, we ought to count the number of rational points over finite fields of these Calabi--Yau threefolds to concoct their L-series. In the other venue, we ought to construct some modular varieties, in this case, conjecturally, Siegel modular forms of weight $3$ and genus $2$ on some paramodular subgroups of $Sp(4,{\bf{Z}})$, and then compute their L-series. Such modular forms may be constructed using Borcherds forms. The ultimate aim is to establish a Langlands correspondence between the two L-series, thereby establishing the modularity/automorphy of such Calabi--Yau threefolds.

This is a joint work with Yifan Yang (National Taiwan University).

Tuesday, October 16th, 2018

Time: 10:15 a.m.  Place: Jeffery Hall 422

Speaker: Siddhi Pathak (Queen's University)

Title: On the Euler-Kronecker constants.

Abstract: Values of the series $\sum_{n=1}^{\infty} A(n)/B(n)$ where A(X) and B(X) are polynomials with suitable conditions to ensure convergence, have been studied by several authors in the past. The evaluation of these series can be considered as a generalization of Euler's theorem evaluating $\zeta(2k)$. In this talk, we study elliptic analogues of these series.

Thursday, October 11th, 2018

Time: 4:30-6:00 p.m.  Place: Jeffery Hall 422

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

Title: Right Hilbert A-modules

Abstract:  Last week, we gave a sketch of proving the GNS construction. We will start to introduce the matrices over a C*-algebra this week, which is an application of the GNS construction. Then, we will begin the new topic: Right Hilbert A-modules. We will deduce the process to construct the inner product on a right Hilbert A-module H. As long as we have the inner product, we can consider the orthogonality on H and compare the different between the scalar case and $A$-valued case.

Free Probability and Random Matrices Seminar Webpage:

Tuesday, October 9th, 2018

Time: 2:00-3:30 p.m Place: Jeffery Hall 116

Speaker: Mike Roth (Queen's University)

Title: Examples of subschemes of points

Abstract: Last time we defined the ‘Hilbert Scheme of points’ of a projective variety $X$. This talk will concentrate on examples of the objects being parameterized. I.e., what is "a subscheme of $X$ with Hilbert polynomial $P(s) = m$?".