Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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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.

Geometry & Representation - Andrew Harder (Lehigh University)

Monday, March 9th, 2020

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 102

Speaker: Andrew Harder (Lehigh University)

Title: Log symplectic pairs and mixed Hodge structures.

Abstract:  A log symplectic pair is a pair (X,Y) consisting of a smooth projective variety X and a divisor Y in X so that there is a non-degenerate log 2-form on X with poles along Y. I will discuss the relationship between log symplectic pairs and degenerations of hyperkaehler varieties, and how this naturally leads to a class of log symplectic pairs called log symplectic pairs of pure weight. I will give examples of families log symplectic pairs of pure weight; one coming from elliptic curves, and one coming from a hybrid toric/cluster construction. Finally, I will explain that if Y is a simple normal crossings divisor, the cohomology of a log symplectic pair (X,Y) is incredibly restricted. In particular, if there are dim(X) components of Y meeting in a point, the cohomology ring of (X,Y) has the "curious hard Lefschetz" property of Hausel and Rodriguez-Villegas.

Department Colloquium - Tim Hoheisel (McGill University)

Tim Hoheisel (McGill University)

Friday, March 6th, 2020

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

Speaker: Tim Hoheisel (McGill University)

Title: Cone-Convexity and Composite Functions.

Abstract: In this talk we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone-convexity, is straightforward. The results are established under a verifiable Slater-type condition, with relaxed monotonicity and without lower semicontinuity assumptions on the functions in play. The versatility of our findings is illustrated by a series of applications in optimization and matrix analysis, including conic programming, matrix-fractional, variational Gram, and spectral functions.

Tim Hoheisel is an Assistant Professor within the Department of Mathematics and Statistics at McGill University. He obtained his Ph.D. in Mathematics from the University of Wuerzburg in 2009. His research lies at the intersection of continuous optimization and nonsmooth analysis and therefore between applied and pure mathematics. The problems on which he works on can be motivated by concrete applications as well as purely conceptual interest.

Dynamics, Geometry, & Groups - Sami Douba (McGill)

Friday, March 6th, 2020

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

Speaker: Sami Douba (McGill)

Title: 2-Systems of arcs on spheres with prescribed endpoints.

Abstract: A 2-system of arcs on an n-punctured sphere S is a collection of (homotopy classes) of essential simple arcs on S joining punctures and pairwise intersecting at most twice. Bar-Natan proved that a 2-system of arcs on S beginning and ending at a fixed puncture has size at most n choose 3. In this talk, I will sketch a proof that the same holds for a 2-system of arcs on S joining a fixed pair of distinct puncture.

Math Club - Anup Dixit (Queen's University)

Thursday, March 5th, 2020

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

Speaker:  Anup Dixit (Queen's University)

Title:  Buffon’s needle problem.

Abstract: In 1734, Buffon asked the following question: If a needle is dropped onto a floor made of parallel wooden planks, what is the probability that it will cross one of the cracks between the planks?

In this talk, we will answer Buffon's question and indicate how it can be used to approximate the value of $\pi$. We will also discuss a few variations of this problem.

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

Wednesday, March 4th, 2020

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

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

Title: Kemeny’s Proof (Part 1).

Abstract: We examine Michael Kemeny's approach for describing the minimal free resolution of a canonical curve of even genus. In the first part, we recast the problem using vector bundles on some auxiliary space.

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