Christine Eagles, University of Waterloo
Zilber dichotomy in DCF_m III
We continue to read Omar Leon Sanchez' paper
MC 5403
Andy Zucker, University of Waterloo
Minimal dynamics of topological groups: A set-theoretic perspective
This talk explores the minimal actions of topological groups on compact spaces. By a classical result of Ellis, every topological group admits a largest such action called the universal minimal flow. Here, we take a set-theoretic perspective and ask how the universal minimal flow can change when considering different models of set theory. In particular, we will take the opportunity to give a gentle introduction to set-theoretic forcing. Our main result is a characterization of those topological groups for which the universal minimal flow is absolute. Joint work with Gianluca Basso.
MC 5501
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