Events

Liam Orovec, University of Waterloo

Greedy beta-expansions for families of Salem numbers

We give criteria for finding the greedy beta-expansion for 1 under families of Salem numbers that approach a given Pisot number. We show these expansions are related to the greedy expansion under the Pisot base. This expands the work of Hare and Tweedle to include more Pisot numbers and more families of Salem numbers.

MC 5403

Faisal Romshoo, University of Waterloo

A canonical form theorem for elements of spin(7)

We will first demonstrate the maximal torus theorem at the Lie algebra level for the exceptional Lie algebra g_2 by proving a canonical form theorem for the elements of g_2 following arXiv:2209.10613. Then, we will proceed to prove a canonical form theorem for the elements of the Lie algebra spin(7).

MC 5479

Erik Seguin, University of Waterloo

Selected Topics on Fourier Algebras of Locally Compact Hausdorff Groups

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

MC 5403

Blake Madill & Zack Cramer, University of Waterloo

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

Miho Mukohara, University of Tokyo

On a Galois correspondence for minimal actions of compact groups on C*-algebras

Inclusions arising from compact quantum group actions on factors have been studied by Izumi-Longo-Popa and Tomatsu. For a minimal action of a compact group on a factor, there is an isomorphism from the lattice of closed subgroups onto that of intermediate subfactors between the factor and the fixed point subfactor. The correspondence between intermediate subfactors and subgroups is called a Galois correspondence. As a duality result, a Galois correspondence for discrete group actions is also known. Analogues for actions on C*-algebras were also studied by Izumi, Cameron-Smith, and others. In this talk, I will discuss a Galois correspondence for compact group actions on C*-algebras. A crucial result for our main theorem is the proper outerness of finite index endomorphisms of purely infinite simple C*-algebras. This was shown by Izumi recently. If time permits, I will also explain an extension of our main result to actions of compact quantum groups of Kac type and a relationship between our main result and the C*-discrete inclusion introduced by Hernández Palomares and Nelson.

MC 5417 or Join on Zoom

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