Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Department Colloquium - Tai-Peng Tsai (University of British Columbia)

Tai-Peng Tsai (University of British Columbia)

Friday, March 13th, 2020

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

Speaker: Tai-Peng Tsai (University of British Columbia)

Title: Discretely self-similar solutions of incompressible Navier-Stokes equations and the local energy class.

Abstract: In this talk, we first review several concepts of solutions of the incompressible Navier-Stokes equations and the questions of regularity and uniqueness. We then introduce forward and backward self-similar solutions and their variants, and the similarity transform. We next sketch a few constructions of forward discretely self-similar (DSS) solutions for arbitrarily large initial data in weak $L^3$ and $L^2$ local. We finally explain their connection to the theory of local energy solutions.

Tai-Peng Tsai graduated from the University of Minnesota under the supervision of Vladimir Sverak. He was a Courant Instructor at the New York University and a Member of the Institute for Advanced Study before he joined the University of British Columbia. He works on the analysis of fluid and dispersive PDEs, including the regularity problem and self-similar solutions of Navier-Stokes equations, the asymptotic behavior of multi-solitons of Schrödinger and gKdV equations, and the regularity of energy critical Schrödinger maps.

Number Theory Seminar - Keshia Yap

Monday, March 16th, 2020

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 422

Speaker: Keshia Yap

Title: Dimension of magic squares over a field.

Abstract: In this talk, we will follow the proof of Charles Small's 1988 paper to compute the dimension of magic squares over fields. A magic square of size $n$ over a field $F$ is an $n \times n$ matrix for which every row, every column, the principal diagonal and the principal backdiagonal all have the same sum. The set of all magic squares is an $F$-vector space. We will prove that for $n \geq 5$, its dimension is $n^2 - 2n$ (for all $F$), and for $n

Dynamics, Geometry, & Groups - Merlin Incerti-Medici

Friday, March 6th, 2020

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

Speaker: Merlin Incerti-Medici (Universität Zürich)

Title: Circumcenter extension maps for Hadamard manifolds.

Abstract: Given a geodesically complete CAT(-1) space, we can associate a boundary at infinity to it. This boundary is equipped with a geometric structure called cross ratio. While it was known for several decades that the boundary together with the cross ratio completely determines the interior space in some special cases, we recently learned that they always roughly determine the interior space. The key tool in this process is a construction called the circumcenter extension. In this talk, we survey known results about the circumcenter extension and show that its construction can be performed in a large class of CAT(0) spaces and still yields interesting results.

Math Club - Troy Day (Queen's University)

Thursday, March 12th, 2020

Time:  5:30 - 6:30 p.m Place: Jeffery Hall 118

Speaker:  Troy Day (Queen's University)

Title:  What does the equation $e^{-2x}=1-x$ have to do with epidemiology?

Abstract: An important goal of epidemiology is to predict the spread of infectious diseases. We will see how relatively simple mathematical models are used to generate such predictions, as well as how they are used to guide public health interventions.

CYMS Seminar - Andrew Harder (Lehigh University)

Thursday, March 12th, 2020

Time: 2:40-4:00 p.m Place: Jeffery Hall 319

Speaker: Andrew Harder (Lehigh University)

Title: Calabi--Yau threefolds fibered K3 surfaces and their mirrors.

Abstract: Mirror symmetry predicts that, given a family of Calabi--Yau varieties, there is a mirror dual family of Calabi--Yau varieties, so that the algebraic aspects of the first are reflected by the symplectic aspects of the other, and vice versa. However, given a family of Calabi--Yau threefolds, it is not usually clear how its mirror family can be constructed. We address this problem for smooth Calabi--Yau threefolds that are built by smoothing degenerate Calabi--Yau threefolds made up of unions of pairs of quasi-Fano manifolds. This leads to a classification of a certain class of Calabi--Yau threefolds, and a surprising relationship to Ishkovskih's famous classification of smooth Fano threefolds of Picard rank 1. This is based on joint work with C. Doran, A. Novoseltsev, and A. Thompson.

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

Wednesday, March 11th, 2020

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

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

Title: Kemeny’s Proof (Part 2).

Abstract: We continue our examination of Michael Kemeny's approach for describing the minimal free resolution of a canonical curve of even genus. In this second part, we establish the needed vanishing for the appropriate cohomology groups.

Probability Seminar - Pei-Lun Tseng (Queen’s University)

Tuesday, March 10th, 2020

Time: 1:30-2:30 p.m.  Place: Jeffery Hall 422

Speaker: Pei-Lun Tseng (Queen’s University)

Title: Infinitesimal Central Limit Theorem.

Abstract:  In this talk, we will review the four notions of infinitesimal independence, and derive associated central limit theorems.

Free Probability and Random Matrices Seminar Webpage:

Topological Data Analysis - Jeffrey Gauthier (Swarthmore)

Monday, March 9th, 2020

Time: 2:30-4:00 p.m. Place: Goodes Hall 120

Speaker: Jeffrey Gauthier (Swarthmore)

Title:  Are we there yet? How hippocampus neurons help us navigate the world.

Jeffrey Gauthier is an Assistant Professor of Biology at Swarthmore. Before thathe was most recently a postdoctoral research associate at the Princeton Neuroscience Institute, examining in vivo measurements of neural activity in awake mice navigating a virtual environment. He also did postdoctoral research at the Salk Institute for Biological Studies, including multielectrode recordings in primate retina to see how color opponency arises from the sampling of individual cones.

Number Theory Seminar - David Wehlau

Monday, March 9th, 2020

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 422

Speaker: David Wehlau

Title: Planes in Finite Fields, Lehmer Numbers and the Multiplicative Order of Elements mod $p$.

Abstract: Let $\mathbb{F}_p$ denote the finite field of order $p$ and $\mathbb{F}$ its algebraic closure. Classifying the $\mathbb{F}$-representations of $\mathbb{Z}/p\mathbb{Z} \times \mathbb{Z}/p\mathbb{Z}$ leads to a simply stated geometric problem involving $\mathbb{F}_p$-planes in $\mathbb{F}$. Solving this leads in turn to an infinite family of polynomials in $\mathbb{F}[t]$. These polynomials have a number of surprising algebraic and combinatorial properties and satisfy a recursion relation related to that studied by D.H. Lehmer in his thesis. This is joint work with H. E. A. Campbell.

This presentation will be accessible to graduate students and senior undergraduates.