Events

Elisabeth Werner, Case Western Reserve University

Affine invariants in convex geometry

In analogy to the classical surface area, a notion of affine surface area (invariant under affine transformations) has been defined. The isoperimetric inequality states that the usual surface area is minimized for a ball. Affine isoperimetric inequality states that affine surface area is maximized for ellipsoids. Due to this inequality and its many other remarkable properties, the affine surface area finds applications in many areas of mathematics and applied mathematics. This has led to intense research in recent years and numerous new directions have been developed. We will discuss some of them and we will show how affine surface area is related to a geometric object, that is interesting in its own right, the floating body.

MC 5501

Robert Cornea, University of Waterloo

Stable Pairs on P2 via Spectral Correspondence

In this talk we will consider stable wild Vafa-Witten-Higgs bundles (or stable pairs for short) (E, ϕ) on P^2 where E is a rank two holomorphic vector bundle and ϕ : E -> E(d) is a holomorphic bundle map with d > 0. There is a way to construct stable pairs on called the spectral correspondence. This states that given a stable pair (E,ϕ) on P^2, there exists a surface Y and a 2:1 covering map pi: Y -> P^2 such that E is the push forward of a line bundle on Y and ϕ comes from the multiplication of a section on Y. So studying stable pairs (E,ϕ) on P^2 boils down to finding 2:1 covering maps Y -> P^2 and line bundles on Y. The study of constructing rank two vector bundles on P^2 via 2:1 coverings was studied by Schwarzenberger in 1960. We will demonstrate examples of stable pairs when d=1 and explain the cases briefly for d=2 and 3.

MC 5479

Noah Slavitch, University of Waterloo

Measurable Cardinals and Non-Constructible Sets

In this talk we will explain how the existence of a measurable cardinal implies that V≠L, that is, that there exist nonconstructible sets.

MC 5479

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