Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Geometry & Representation - Atabey Kaygun (Istanbul Tech University)

Monday, September 23rd, 2019

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 319

Speaker: Atabey Kaygun (Istanbul Technical University)

Title: Distributive Laws, Smash Biproducts and Hochschild Homology.

Abstract:  In this talk I am going to talk about distributive laws between algebras, resulting smash biproducts and their Hochschild homology. The examples include Ore extensions, Hopf smash products, quantum affine spaces and quantum complete intersection algebras. This is joint work with Serkan Sutlu.

Department Colloquium - Xudong Chen (CU Boulder)

Xudong Chen (CU Boulder)

Friday, September 20th, 2019

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

Speaker: Xudong Chen (CU Boulder)

Title: Structure Theory for Ensemble Control and Estimation of Nonholonomic Systems.

Abstract: Ensemble control deals with the problem of using a finite number of control inputs to simultaneously steer a large population (in the limit, a continuum) of individual control systems. As a dual, ensemble estimation deals with the problem of using a finite number of measurement outputs to estimate the initial state of every individual system in the (continuum) ensemble. We introduce in the talk a novel class of ensembles of nonlinear control systems, termed distinguished ensemble systems. Every such system has two key components, namely a set of finely structured control vector fields and a set of co-structured observation functions. In the first half of the talk, we demonstrate that the structure of a distinguished ensemble system can significantly simplify the analysis of ensemble controllability and observability. Moreover, such a structure can be used as a principle for ensemble system design. In the second half of the talk, we address the issue about existence of a distinguished ensemble system for a given manifold. We will focus on the case where the underlying space of every individual system is an arbitrary semi-simple Lie group or its homogeneous space.

Professor Chen is an Assistant Professor at the University of Colorado, Boulder. Before that, he was a postdoctoral fellow in the Coordinated Science Lab at UIUC. He obtained his Ph.D. degree in Electrical Engineering from Harvard University in 2014. His research interests are in the area of control theory, stochastic processes, optimization, game theory and their applications in modeling and control of large-scale networked systems.

Dynamics, Geometry, & Groups - Ian Frankel (Queen's University)

Friday, September 20th, 2019

Time: 10:30 a.m Place: Jeffery Hall 319

Speaker: Ian Frankel (Queen's University)

Title: Local geometry of Teichmüller space: flat and quasiconformal.

Abstract: The Teichmüller distance between two homeomorphic Riemann surfaces X and Y is a number that quantifies the following question: Given a homeomorphism from X to Y, how non-conformal does the map have to be?

The optimal quasiconformal maps, i.e. those with smallest quasiconformal constant, are characterized by choices of special singular flat metrics on X and Y, and in fact fit into a large familes of maps, and the dynamics of SL(2,R) acting on this family have been the subject of many celebrated results in the past decade.

Now, suppose we are given X and Y but with singular flat metrics that are not related to the optimal map. We will describe how we can still estimate the Teichmüller distance from X to Y.

Curves Seminar—Gregory G. Smith (Queen's University)

Wednesday, September 18th, 2019

Time: 4:00-5:30 p.m.   Place: Jeffery Hall 319

Speaker: Gregory G. Smith (Queen's University)

Title: Koszul complexes

Abstract: We introduce Koszul complexes and examine a couple different interpretations.  Beyond providing a concrete family of minimal free resolutions, this structure plays a significant role in analyzing the syzygies of canonical curves.

Number Theory Seminar - Anup Dixit (Queen's University)

Tuesday, September 17th, 2019

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 319

Speaker: Anup Dixit (Queen's University)

Title: On Euler-Kronecker constants and the prime number theorem.

Abstract: As a generalization of the Euler-Mascheroni constant $\gamma$, Y. Ihara defined the the Euler-Kronecker constant $\gamma_K$ attached to a number field $K/\mathbb{Q}$. Ihara conjectured that for a cyclotomic fields $K$, $\gamma_K >0$. This initiated the study of the bounds on $\gamma_K$ for cyclotomic fields. In this talk, we describe an application of these bounds to the error term in the prime number theorem for certain arithmetic progressions. This is joint work with Prof. M. Ram Murty.

Department Colloquium - Sarah Mayes-Tang (University of Toronto)

Sarah Mayes-Tang (University of Toronto)

Friday, September 13th, 2019

Time: 2:30 p.m.  Place: Jeffery Hall 127

Speaker: Sarah Mayes-Tang (University of Toronto)

Title: Why We Share Our Stories: Identity, Participation, and Celebration of Women in Math.

Abstract: Despite remarkable contributions by women mathematicians, the participation and recognition of women in mathematics remains unacceptably low. Women are usually excluded from the popular images of mathematicians, and the number of women in our academic departments lags behind most other STEM disciplines. How can we transform mathematics into a field where women are accepted, valued, and visible? In this talk, I will argue that mathematical stories shape participation in mathematics and I will advocate for the value of celebrating stories of women mathematicians, amplifying stories of girls and women doing mathematics, and sharing our own stories.

Professor Sarah Mayes-Tang is a Queen's alumni, she then got her Ph.D. at the University of Michigan and worked at Quest University before moving to the University of Toronto in 2017. Her research interests are in commutative algebra and in Mathematics education.

Dynamics, Geometry, & Groups - James Mingo (Queen's University)

Friday, September 13th, 2019

Time: 10:30 a.m Place: Jeffery Hall 319

Speaker: James Mingo (Queen's University)

Title: Can a free group have a fractional number of generators? In the free world it can.

Abstract: Starting with a countable discrete group G we complete the group ring in a suitable topology to get L(G), the group von Neumann algebra. We let L(n) be the group von Neumann algebra for the free group on n ≥ 2 generators. Using random matrix theory Voiculescu showed that if we tensor L(m) with the k x k matrices we get an algebra isomorphic to L(n). The relation between k, m, and n is the same as in Schreier's index theorem for subgroups of free groups. With this we can define L(t) for any real t > 1 as the group algebra of the free group with t generators. I will explain the main ideas in the proof. No prior knowledge of free probability will be assumed.

Curves Seminar—Gregory G. Smith (Queen's University)

Wednesday, September 11th, 2019

Time: 4:00-5:30 p.m.   Place: Jeffery Hall 319

Speaker: Gregory G. Smith (Queen's University)

Title: Minimal free resolutions

Abstract: With the year-long objective of understanding the syzygies of generic canonical curves, we begin with a gentle introduction to minimal free resolutions of homogeneous ideals in a standard graded polynomial ring.

Number Theory Seminar - Seoyoung Kim (Queen's University)

Tuesday, September 10th, 2019

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 319

Speaker: Seoyoung Kim (Queen's University)

Title: The Sato-Tate conjecture and Nagao’s conjecture.

Abstract: Nagao’s conjecture relates the rank of an elliptic surface to a limit formula arising from a weighted average of fibral Frobenius traces, and it is further generalized for smooth irreducible projective surfaces by Hindry and Pacheco. We show that the Sato-Tate conjecture for abelian surfaces studied by Fit\'{e}, Kedlaya, Rotger, Sutherland implies Nagao’s conjecture for certain twist families hyperelliptic curves of genus 2. Moreover, one can relate analogous discussions for higher genus g to the non-vanishing result on the symmetric power $L$-functions, from which analogous proof will hold for certain cases.