Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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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.

Department Colloquium - Bahman Gharesifard (Queen's University)

Bahman Gharesifard (Queen's University)

Friday, September 6th, 2019

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

Speaker: Bahman Gharesifard (Queen's University)

Title: Fundamental Limits in Control and Optimization of Networked Systems.

Abstract: The emergence of network sciences within the disciplines of engineering, biological, and social systems has revealed numerous opportunities for sensing and feedback. This development, together with the availability of an abundance of useful data, has provided capabilities that allow for the execution of remarkably complex tasks, which cannot be handled by individual systems. I will provide an overview of some of the recent advancements on control and optimization of large-scale networked systems, mathematically modelled as dynamical systems with external inputs over graphs. The talk will focus on fundamental limits to decentralization; I will show graph-theoretic conditions that decentralization imposes on the controllability and stabilization of sparse systems, as well as a class of submodoular optimization problems. One key objective throughout the talk is to showcase the versatile set of mathematical tools that naturally enter the study of networked systems.

CYMS Seminar - Richard Gottesman (Queen's University)

Thursday, September 5th, 2019

Time: 2:30 p.m Place: Jeffery Hall 319

Speaker: Richard Gottesman (Queen's University)

Title: Vector-Valued Modular Forms and Modular Linear Differential Equations

Abstract: The sequence of denominators of the Fourier coefficients of a modular form on a congruence subgroup is always bounded. It has been conjectured that the converse is also true. We will consider this problem in the context of vector-valued modular forms and explain a strategy for proving such an unbounded denominator result. A key point is the importance of understanding the solutions of the modular linear differential equation at all of the cusps).

Dynamics, Geometry, & Groups - Catherine Pfaff (Queen's University)

Tuesday, August 27th, 2019

Time: 1:30 p.m Place: Jeffery Hall 319

Speaker: Catherine Pfaff (Queen's University)

Title: Typical Trees: An Out(F_r) Excursion.

Abstract: Random walks are not new to geometric group theory (see, for example, work of Furstenberg, Kaimonovich, Masur). However, following independent proofs by Maher and Rivin that pseudo-Anosovs are generic within mapping class groups, and then new techniques developed by Maher-Tiozzo, Sisto, and others, the field has seen in the past decade a veritable explosion of results. In a 2 paper series, we answer with fine detail a question posed by Handel-Mosher asking about invariants of generic outer automorphisms of free groups and then a question posed by Bestvina as to properties of R-trees of full measure in the boundary of Culler-Vogtmann outer space. This is joint work with Ilya Kapovich, Joseph Maher, and Samuel J. Taylor.