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Number Theory Seminar

Tuesday, November 21st, 2023

Time: 4:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Grayson Plumpton (Queen's University)

Title: Some probability laws concerning the Dedekind zeta functions of $\mathbb{Q}$, $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-2})$.

Abstract: This talk is a follow up to a talk given at the number theory seminar in winter 2023, in which we introduce the paper “Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions” by Phillipe Biane, Jim Pitman, and Marc Yor. In this talk, we will reframe some ideas from this paper using the language of Tate-Iwasawa theory, and use this to give a probabilistic interpretation of the Dedekind zeta functions of the fields $\mathbb{Q}$, $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-2})$.

Math & Stats Department Colloquium

Friday, November 17th, 2023

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

Speaker: Felicia Magpantay (���ϳԹ���Դ)

Title: Challenges in modeling the transmission dynamics of childhood diseases

Abstract: Mathematical models of childhood diseases are often fitted using deterministic methods under the assumption of homogeneous contact rates within populations. Such models can provide good agreement with data in the absence of significant changes in population demography or transmission, such as in the case of pre-vaccine era measles. However, accurate modeling and forecasting after the start of mass vaccination have proven to be more challenging. This is true even in the case of measles which has a well understood natural history and a very effective vaccine. We demonstrate how the dynamics of homogeneous and age-structured models can be similar in the absence of vaccination, but diverge after vaccine roll-out. We also present the different methods used to fit deterministic and stochastic models, and propose new techniques to fit long term time series with imperfect covariate information. The methods we develop can be applied to many types of complex systems beyond those in disease ecology.

Bio: Prof. Felicia Magpantay is an Associate Professor here at ���ϳԹ���Դ, working in the fields of mathematical modeling and biomathematics, as well as differential equations, applied dynamics and applied probability. Prof. Magpantay obtained her Ph.D. in 2012 from McGill, then held postdoctoral positions at York University and the University of Michigan, and an assistant professor position at the University of Manitoba before joining ���ϳԹ���Դ in 2017.

Curves Seminar

Thursday, November 16th, 2023

Time: 4:00 p.m.  Place: Jeffery Hall, Room 102

Speaker: Sonja Ruzic

Title: Y-patterns: Motivation and examples

Abstract: Last week we were briefly introduced to Y-patterns. In this talk, we will study Y-patterns more extensively and seek to understand why they are important, both as an independent object of study but also in comparison to ordinary patterns. In order to help motivate Y-patterns further, we will study several examples.

Number Theory Seminar

Tuesday, November 14th, 2023

Time: 3:30 p.m.  Place: Jeffery Hall, Room 102

Speaker: V. Kumar Murty (Fields Institute and U of T)

Title: Pair correlation and the Chebotarev density theorem

Abstract: We describe a pair correlation hypothesis for Artin L-functions and discuss the implications for the error term in the Chebotarev density theorem. We then discuss what can be proved about the hypothesis itself.

Dynamics, Geometry and Groups Seminar

Monday, November 13th, 2023

Time: 11:00 a.m.  Place: Jeffery Hall, Room 319

Speaker: Annika Fuernsinn (Queen's University)

Title: Towards Model Predictive Control

Abstract: In this talk, I provide some insights into my research for non-control mathematicians. We start with dynamical systems, but then enter into the control world and try to solve an infinite-horizon optimal control problem. As it turns out, this is quite a difficult problem and we can instead approximate the solution by considering the framework of Model Predictive Control (MPC). In the remaining talk we will discuss some shortcomings of MPC and try to provide resolutions. The idea is to introduce some flexibility into the standard MPC scheme, from which we deduce the novel flexible-step MPC scheme.

Curves Seminar

Thursday, November 9th, 2023

Time: 4:00 p.m.  Place: Jeffery Hall, Room 102

Speaker: Sonja Ruzic

Title: More Examples and Laurent Polynomials

Abstract: Last week we noticed that each cluster variable can be expressed as a Laurent polynomial with integer coefficients in the elements of any extended cluster. This week we will see why that is the case, and we will look at some more examples of rank 2 cluster algebras.

Number Theory Seminar

Tuesday, November 7th, 2023

Time: 4:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: M. Ram Murty (Queen's University)

Title: HIGHER CONVOLUTIONS OF RAMANUJAN SUMS

Abstract: We will discuss limit formulas for higher convolutions of Ramanujan sums and give applications to present a heuristic derivation of the Hardy-Littlewood conjectural formula for the number of k-tuples of primes. This is joint work with Shivani Goel.

Math & Stats Department Colloquium

Friday, November 3rd, 2023

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

Speaker: Jessica Lin (McGill University)

Title: Quantitative Homogenization for Nondivergence Form Equations

Abstract: In this talk, I will first give an introduction to stochastic homogenization for nondivergence form elliptic equations (from the PDE perspective) and quenched invariance principles for nonreversible diffusion processes (from the probability perspective). I will then present new quantitative homogenization results for the fundamental solution and the unique ergodic invariant measure. I will discuss the implications of these homogenization results, such as heat kernel bounds on the fundamental solution and quantitative ergodicity for the environmental process. This talk is based on joint work with Scott Armstrong (NYU) and Benjamin Fehrman (LSU).

Bio: Prof. Jessica Lin is an Associate Professor at McGill University and a CRC in Partial Differential Equations and Probability. Before McGill, she received her PhD from the University of Chicago and did a postdoc at the University of Wisconsin–Madison. Her research is broadly focused on the asymptotic behaviour of random physical systems, with an emphasis on stochastic homogenization, limit theorems, and effective phase transitions in various models subject to randomness.

Curves Seminar

Thursday, November 2nd, 2023

Time: 4:00 p.m.  Place: Jeffery Hall, Room 102

Speaker: Alexandre (Sasha) Zotine

Title: Examples of Cluster Algebras

Abstract: We'll look at several examples of cluster algebras in order to soak in the definition. We will also discuss some remarks about the definition.

Number Theory Seminar

Tuesday, October 31st, 2023

Time: 4:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Abhishek Bharadwaj (Queen's University)

Title: Algebraic Numbers with Integral Power Traces

Abstract: In this paper, the following result is proved : To determine if an algebraic number \alpha of degree n is an algebraic integer, it suffices to show that the trace of the powers \alpha^i is an integer for all positive i up to n + n log2n. We shall describe the key ingredients of the proof.