A new $1.3 million professorship will bring more experiential learning, outreach, and groundbreaking research to the Department of Mathematics and Statistics.
Date
Friday February 14, 2025Location
319 JEFFERY HALLFriday, February 14, 2025
Time: 10:30 a.m. Place: Jeffery Hall, Room 319
Speaker: Alexey Shevyakov (University of Saskatchewan)
Title: Conservation laws of differential equations: computation, connections, and applications
Abstract: Local conservation laws of a system of differential equations (DE) are given by one or several divergence expressions that hold on solutions of that system. For ordinary differential equations, conservation laws lead to first integrals and the reduction of order. For partial differential equations (PDE), they provide globally conserved quantities, such as energy, momentum, as well as more exotic ones. Conservation laws used for analysis of global solution behaviour, are related to multiple other analytical properties of PDEs, and play an important role in the numerical treatment of PDEs.
In this talk, we will review the general theory, including trivial and equivalent conservation laws, their characteristic form, relationships with integrability, symmetries of DEs, Hamiltonians, variational systems, Lagrangians, and the first and second Noether's theorems. A systematic procedure to seek conservation laws will be discussed, applicable to virtually any PDE system; it will be compared to the Noether's theorem approach to seek conservation laws of variational models. A symbolic implementation of the direct method of conservation law computation in Maple will be presented. Examples of conservation laws and conserved quantities for classical PDEs and some nonlinear models arising in contemporary work will be discussed.
Time permitting, we will consider a common framework for different types of conservation laws of PDE systems in three space dimensions, including their global and local formulations in static and moving domains given by volumes, surfaces, and curves.
Date
Friday February 14, 2025Location
Jeffrey Hall, Room 234Math & Stats Department Colloquium
Friday, February 14, 2025
Time: 2:30 p.m. Place: Jeffery Hall, Room 234
Speaker: Alexey Shevyakov (University of Saskatchewan)
Title: Spatiotemporal Behaviour of SIR Models with Cross-Diffusion and Vital Dynamics
Abstract: Contemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements. In this work, we extend a recent model by Vaziry, Kolokolnikov, and Kevrekidis [Royal Society Open Science 9 (10), 2022] that included, in both infected and susceptible population dynamics equations, a cross-diffusion term with the second spatial derivative of the infected population density. Diffusion terms of this type occur, for example, in the Keller-Siegel chemotaxis model. The presented model corresponds to local orderly commute of susceptible and infected individuals, and is shown to arise in two dimensions as a limit of a discrete process. The present contribution identifies and studies specific features of the new model's dynamics, including various types of infection waves and buffer zones protected from the infection. The model with vital dynamics additionally exhibits complex spatiotemporal behaviour that involves the generation of quasiperiodic infection waves and emergence of transient strongly heterogeneous patterns.
Date
Friday February 7, 2025Location
319 JEFFERY HALLFriday, February 7, 2025
Time: 10:30 a.m. Place: Jeffery Hall, Room 319
Speaker: Jerin Tasnim Farin (Queen's University)
Title: Regularity of solutions to the Navier equations with mixed boundary conditions
Abstract: In this talk, I will present some regularity results for the partial differential equations that model the deformations of an elastic material. These equations are known as the Navier equations of linear elasticity. We impose mixed (Dirichlet and Neumann-type) boundary conditions on the solid's boundary. More precisely, we assume that the boundary of the solid is constituted by two disjoint components: an “interior" one subject to a non-zero displacement (a Dirichlet boundary condition), and an “exterior" one subject to a traction-free boundary condition (a Neumann-type condition). We will demonstrate existence and uniqueness of the solution to the relevant initial-boundary value problem in a weak sense and derive some additional regularity of the traction vector on the boundary. The classical energy estimates do not yield such a regularity result; it is in the spirit of the "hidden regularity" shown for solutions to the wave equation with Dirichlet boundary conditions.
Date
Thursday February 6, 2025Location
Jeffery Hall, Room 118Thursday, February 6th, 2025
Time: 5:30 p.m. Place: Jeffery Hall, Room 118
Speaker: Mike Roth (Queen's University)
Title: Pseudorandom number generation and the NSA backdoor
Abstract: This talk will discuss a specific method in the US crypographics standards for producing pseudorandom numbers, and the backdoor in that method (apparently introduced by the NSA).
Date
Thursday January 30, 2025Location
Jeffery Hall, Room 118Thursday, January 30th, 2025
Time: 5:30 p.m. Place: Jeffery Hall, Room 118
Speaker: Gregory G. Smith
Title: Domino Tilings
Abstract: How many different ways can one cover a chess board with dominos? To develop a combinatorial formula, we will exploit linear algebra (over the complex numbers) to produce an unexpected product.
Date
Thursday January 23, 2025Location
Jeffery Hall, Room 118Thursday, January 23rd, 2025
Time: 5:30 p.m. Place: Jeffery Hall, Room 118
Speaker: Ram Murty (Queen's University)
Title: The 2-adic logarithm
Abstract: We will discuss how to make sense of the equation
$$\sum_{n=1}^\infty \frac{2^n}{n} = 0, $$
by entering the 2-adic world and studying the analog of the logarithm function there. In the process, we will discover there is a spectrum of p-adic worlds, one for each prime number p. Like presiding deities of the known universe of numbers, these worlds hold many hidden secrets!
Date
Wednesday February 5, 2025Location
Jeffery Hall, Room 319Wednesday, February 5, 2025
Time: 3:00 p.m. Place: Jeffery Hall, Room 319
Speaker: Luke Steverango
Title: Initial Ideals of Lattice Ideals
Abstract: In this talk we will discuss the initial monomial ideals of the lattice ideals. These will correspond to Gröbner degeneration of the varieties we have been considering and combinatorially to the decomposition of the semigroup Q.
Date
Friday February 7, 2025Location
Jeffrey Hall, Room 234Math & Stats Department Colloquium
Friday, February 7, 2025
Time: 2:30 p.m. Place: Jeffery Hall, Room 234
Speaker: Michael Groechenig (University of Toronto)
Title: Moduli, mirror symmetry and $p$-adic integration
Abstract: I will report on joint work with Wyss \& Ziegler on $p$-adic integration for moduli spaces of Higgs bundles. After introducing Higgs bundles and Hitchin systems we will discuss how $p$-adic integration can be used as a tool to establish mirror symmetry phenomena for these. Subsequently, I will explain how this sheds new light on the Fundamental Lemma (previously proven by Ngô). I will conclude the talk by describing our recent results which apply $p$-adic integration to new kinds of moduli problems and provide a connection to DT-theory.
Date
Wednesday January 29, 2025Location
Jeffery Hall, Room 319Wednesday, January 29, 2025
Time: 3:00 p.m. Place: Jeffery Hall, Room 319
Speaker: Calvin Fletcher
Title: Hilbert Bases
Abstract: Given a rational cone, we can associate to it an affine semigroup. This result, referred to as Gordan's Lemma allows us to define a Hilbert basis for a rational cone. After computing some examples of Hilbert bases, we will turn to the question of how one computes a Hilbert basis. There is an algebraic solution to the problem, making use of Lawerence ideals. Finally, we will introduce the notion of saturation and its relationship to the normalization of the affine semigroup ring.
