Events

Emily Quesada-Herrera, University of Lethbridge

Fourier optimization and the least quadratic non-residue

We will explore how a Fourier optimization framework may be used to study two classical problems in number theory involving Dirichlet characters: The problem of estimating the least character non-residue; and the problem of estimating the least prime in an arithmetic progression. In particular, we show how this Fourier framework leads to subtle, but conceptually interesting, improvements on the best current asymptotic bounds under the Generalized Riemann Hypothesis, given by Lamzouri, Li, and Soundararajan. Based on joint work with Emanuel Carneiro, Micah Milinovich, and Antonio Ramos.

MC 5479

Kuntal Banerjee, University of Waterloo

Very stable and wobbly loci for elliptic curves

We explore very stable and wobbly bundles, twisted in a particular sense by a line bundle, over complex algebraic curves of genus 1. We verify that twisted stable bundles on an elliptic curve are not very stable for any positive twist. We utilize semistability of trivially twisted very stable bundles to prove that the wobbly locus is always a divisor in the moduli space of semistable bundles on a genus 1 curve. We prove, by extension, a conjecture regarding the closedness and dimension of the wobbly locus in this setting. This conjecture was originally formulated by Drinfeld in higher genus.

MC 5479

Spencer Unger, University of Toronto

Proofs of countable Ramsey theorems

We discuss the various proofs of Ramsey theorems involving colorings of countable sets with additional structure.  To illustrate a typical argument which proves an infinite Ramsey statement from a finite one, we sketch Baumgartner's proof of Hindman's theorem and report on some ongoing related projects.

MC 5479

Veronika Shelestunova, RBC Capital Markets

Teaching Stream

The Career Talks seminar series invites professionals from various fields to share their personal career journeys and insights on how they achieved success. Each session offers valuable advice and guidance for current graduate students. By hearing firsthand experiences, attendees gain a deeper understanding of the challenges and opportunities that lie ahead in their professional lives.

MC 5501

Refreshments will be available during the talk

Amanda Maria Petcu, University of Waterloo

A hypersymplectic structure on R^4 with an SO(4) action

Given a hypersymplectic manifold X^4, one can give a flow of hypersymplectic structures that evolve according to the equation

d_t w = d(Q d^*(Q^{-1} w), where w is the triple that gives the hypersymplectic structure and Q is a 3x3 symmetric matrix. In this talk we let X^4 be R^4 with an SO(4) action  The flow of the hypersymplectic triple then descends to a single flow of a function h. We will examine this flow, as well as solitons of the hypersymplectic flow in this set up. Furthermore, the triple w gives rise to a Riemannian metric g . We will conclude with a discussion about the Riemann and Ricci curvature tensors that are derived from this metric.

MC 5479

Erik Séguin, University of Waterloo

Selected Topics on Fourier-Stieltjes Algebras of Locally Compact Hausdorff Groups.

We discuss some selected topics on Fourier-Stieltjes algebras of locally compact Hausdorff groups.

MC 5403

Meenakshi McNamara, Perimeter Institute for Theoretical Physics

Exact quantum chromatic numbers of Hadamard graphs and products

Quantum chromatic numbers are defined in terms of non-local games on graphs. This talk gives a proof of the exact quantum chromatic number of Hadamard graphs using a conjugacy class graphs approach. This further allows us to consider graph products, and we compute the exact quantum chromatic number of the categorical product of Hadamard graphs. This work makes use of several results for the quantum chromatic numbers of quantum graphs, an operator algebraic generalizations of graphs. In particular, we also discuss results on products of quantum graphs from joint work with Rolando de Santiago.

MC 5417

Christine Eagles, University of Waterloo

Curve excluding fields IV

We continue to read Omar Leon Sanchez' paper.

MC 5403

Xinle Dai, Harvard University

Sectorial Decompositions of Symmetric Products and Homological Mirror Symmetry

Symmetric products of Riemann surfaces play a crucial role in symplectic geometry and low-dimensional topology. They are essential ingredients for defining Heegaard Floer homology and serve as important examples of Liouville manifolds when the surfaces are open. In this talk, I will discuss ongoing work on the symplectic topology of these spaces through Liouville sectorial methods, along with examples as applications of this decomposition construction to homological mirror symmetry.

MC 5417

Adrian Dawid, University of Cambridge

A promenade along the A-side

In this talk we will take a closer look at some of the structures that live on the A-side of mirror symmetry. In particular, the Fukaya category and symplectic cohomology. Along the way we will look at concrete examples of homological mirror symmetry. After a reminder about the Fukaya category, we will introduce symplectic cohomology. We will then discuss the relationship between these two given by open-closed and closed-open string maps. We will look at some examples with an emphasis on the mirror symmetry perspective. If time permits, we will also take a look at some structures that do not (yet?) have an obvious analogue under mirror symmetry, such as the action filtration of the Fukaya category and related invariants.

MC 2017