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Number Theory Seminar

Monday, March 27th, 2023

Time: 4:30 p.m.  Place: Jeffery Hall, Room 319

Speaker: Dominic Austria (Queen's University)

Title: Congruent Numbers and Tunnell’s Theorem

Abstract: We will discuss congruent numbers, their relation to elliptic curves, and some known results about the congruent number problem. The focus will be on outlining the proof of Tunnell’s theorem. We discuss the key tools needed for this--the L-function of a particular elliptic curve associated with the congruent number problem, and modular forms, of both integer weight and half integer weight. We will then see how results on both of these topics can be combined, using the theorems of Shimura and Waldspurger, to classify the congruent numbers up to conjecture.

Probability Seminar

Wednesday, March 22nd, 2023

Time: 12:00 p.m.  Place: Jeffery Hall, Room 234

Speaker: Elizabeth Collins-Woodfin (McGill)

Title: Phase transitions in spherical spin glass models

Abstract: This talk will focus on a series of recent results involving phase transitions in the spherical Sherrington-Kirkpatrick (SSK) spin glass model. In addition to their physical meaning, these phase transitions can be interpreted in the context of statistics, random matrix theory, and optimization problems. In the first half of the talk, I will discuss the transition between SSK with an external field and SSK without an external field (based on my joint work with Baik, le Doussal, Wu). In the second half of the talk, I will discuss the transition between high and low temperature SSK. Recent papers by Landon and by Johnstone-Klochkov-Onatski-Pavlyshyn have analyzed the free energy fluctuations of SSK at the critical temperature. I will summarize these papers and then discuss my current work to extend their result to a bipartite spin glass model (joint with Le). While the context for all of these works is spin glass, my focus is primarily theoretical and draws on tools from random matrix theory, as well as contour integral analysis.

Curves Seminar

Wednesday, March 22nd, 2023

Time: 1:00 p.m.  Place: Jeffery Hall, Room 222 & Zoom

Speaker: Alexandre (Sasha) Zotine

Title: Toric Variety of a Fan

Abstract: We'll see how we can glue affine varieties coming from the cones of a fan to construct a toric variety.

Algebra & Geometry Seminar

Tuesday, March 27th, 2023

Time: 4:30 p.m.  Place: Jeffery Hall, Room 222

Speaker: David Wehlau (RMC & ºÚÁϳԹÏ×ÊÔ´)

Title: Rings of invariants of Finite Classical Groups

Abstract:

Website details here: https://mast.queensu.ca/~georep/Fall%20'22.html

Math Club

Thursday, March 23rd, 2023

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

Speaker: Teresa Chiri (Queen's University)

Title: Dido's Problem: from the foundation of Carthage to the eradication of plant diseases

Abstract: In this talk we will trace the isoperimetric problem from Queen Dido to some recent applications. We will discover why we need to study the calculus of variations to construct a larger town, to create more sophisticated materials, and to fight plant diseases

Number Theory Seminar

Monday, March 20th, 2023

Time: 4:30 p.m.  Place: Jeffery Hall, Room 319

Speaker: Kevin Kwan (University College London)

Title: Some Aspects of Moments

Abstract: In the past century, moments of L-functions have been important in number theory and are well-motivated by a variety of arithmetic applications. In this talk, we will begin with two elementary counting problems of Diophantine nature as motivation, followed by a survey of techniques in the past and the present. The main goal is to demonstrate how period integrals can be used to study moments of automorphic L-functions and uncover the interesting underlying structures (some of them can be modeled by random matrix theory).

Math & Stats Department Colloquium

Friday, March 24th, 2023

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

Speaker: Kevin Kwan (University College London)

Title: A Moment of Duality

Abstract: In this talk, we will discuss some modern perspectives on several classical problems of arithmetic nature dated back to Gauss, Legendre and Dirichlet. We will motivate this subject by concrete questions of dynamical flavors which demonstrate how the presence of "arithmetic" on the manifolds in question (say in terms of group actions, automorphy and duality) can provide elegant solutions to these problems. These problems are furnished by the many connections to spectral theory, harmonic analysis and differential geometry.

Chung-Hang (Kevin) Kwan is currently a research fellow at University College London. He received his Ph.D. from Columbia University in 2022 and his Ph.D. supervisor is Prof. Dorian Goldfeld. He is interested in automorphic forms/ representations/ L-functions and their applications in number theory.

Math Club

Thursday, March 16th, 2023

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

Speaker: Jamie Mingo (Queen's University)

Title: Möbius and his Inversions

Abstract: Motivated by a question on power series, Möbius was led to develop the theory of the Möbius function, as it is now known. This function has may uses in number theory and combinatorics.

We will discuss some of the theory of Möbius functions, concentrating on the combinatorial applications.

Curves Seminar

Wednesday, March 15th, 2023

Time: 1:00 p.m.  Place: Jeffery Hall, Room 222 & Zoom

Speaker: Alexandre (Sasha) Zotine

Title: Properties of Projective Toric Varieties

Abstract: We'll continue with some more examples of how polytopes give projective toric varieties. Afterwards, we'll see how properties of the polytope reflect properties of the variety.

Algebra & Geometry Seminar

Tuesday, March 21st, 2023

Time: 1:00 p.m.  Place: Jeffery Hall, Room 222

Speaker: Francis Bischoff (University of Oxford)

Title: The derived moduli stack of logarithmic flat connections

Abstract:

Website details here: https://mast.queensu.ca/~georep/Fall%20'22.html