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Riley Thornton, Carnegie Mellon University

Topological weak containment

Weak containment is a notion from ergodic theory with a wide variety of applications-- in dynamics, combinatorics, group theory, model theory, and beyond-- and a correspondingly wide variety of equivalent definitions. In this talk, I'll report on a project to adapt the theory to topological dynamics.

MC 5479

Jesse Huang, University of Waterloo

Birational coherent constructible correspondence

A major progress towards the Homological Mirror Symmetry (HMS) conjecture of Kontsevich is a version of HMS for toric varieties proved by Fang-Liu-Treumann-Zaslow and Kuwagaki using constructible sheaves, following an approach originally introduced by Bondal. These results suggest that Bondal's approach can be reinvested as a powerful tool to investigate fundamental algebraic questions pertaining to the birational geometry of toric varieties, and have inspired recent works of Hanlon-Hicks-Lazarev and my works with Favero, both used Bondal's map to obtain short resolutions of the diagonal by a specific collection of line bundles. In this talk, I will discuss these results and their connections to noncommutative resolutions of toric singularities and the broader goal to establish birational toric HMS.

MC 5417

Jacques Van Wyk, University of Waterloo

“The” Generalised Levi-Civita Connection

I will discuss the notions of generalised metrics and generalised connections in generalised geometry. A generalised connection has an associated torsion tensor, so one may ask, if given a generalised metric G, whether there is a torsion-free connection D compatible with G; this is the analogue of the Levi-Civita connection. We will see that there are infinitely many such connections D, that is, there is no unique “generalised Levi-Civita connection,” a striking difference from the situation for Riemannian geometry.

MC 5479

David McKinnon, University of Waterloo

How crowded can rational solutions be?

Say you've got the equation x^2-2y^2=z^4-1. Lots of rational solutions there, like (1,1,0). How are those solutions distributed in 3-space? In particular, how close can they get to (1,1,0)? This abstract has the questions, but the talk has the answers. Well, some of 'em.

MC 5479

Adina Goldberg, University of Waterloo

Categorical Strings for Quantum Things

Heard of quantum graphs or quantum groups? Wondering if this is the same as the "physics" notion of quantum, as in quantum entanglement or quantum channels? When I started my PhD, I was perplexed. Now, some years of marinating in the stew of categorical quantum mechanics has convinced me of its descriptive power for tackling all things quantum. I will show you the string-diagram interface that goes hand-in-hand with dagger (compact/symmetric monoidal) categories, and give examples. Prerequisites: Familiarity with the vague idea of a category, and a willingness to wave your hands a little bit.

MC 5501

Viktor Majewski, Humboldt University Berlin

Resolutions of Spin(7)-Orbifolds

In Joyce’s seminal work, he constructed the first examples of compact manifolds with exceptional holonomy by resolving flat orbifolds. Recently, Joyce and Karigiannis generalised these ideas in the G2 setting to orbifolds with Z2-singular strata. In this talk I will present a generalisation of these ideas to Spin(7) orbifolds and more general isotropy types. I will highlight the main aspects of the construction and the analytical difficulties.

MC 5479

Adina Goldberg, University of Waterloo

Synchronous Quantum Games

We recast nonlocal games using string diagrams, allowing for a natural extension to quantum games (with bipartite question and answer states). We define strategies in this setting and show that synchronous quantum games require synchronized players to win. We give examples of some quantum games on quantum graphs and see that these require quantum homo/isomorphisms to win. (The talk is based on a preprint ``Quantum games and synchronicity'' (https://arxiv.org/abs/2408.15444). This work is inspired by Musto, Reutter, and Verdon's paper ``A compositional approach to quantum functions'', and relies heavily on the reference ``Categories for Quantum Theory'' by Heunen and Vicary for string diagrams in quantum information.)

MC 5417

Matthew Harrison-Trainor, University of Illinois Chicago

Scott analysis of linear orders

The Scott analysis measures the complexity of describing a structure up to isomorphism, and equivalently the complexity of describing its automorphism orbits, and of computing isomorphisms between different copies. I will introduce the Scott analysis in general and talk about the Scott analysis of linear orders in particular. Linear orders have a few special properties which makes their behaviour quite interesting and sometimes different from structures in general.

MC 5479

Cynthia Dai, University of Waterloo

Height Modulis on Toric Stacks

In this talk we will go through Matt’s work on height modulis on weighted projective space, mainly its construction, and then its application. If time permits, I will talk about generalizations of this construction to toric stacks.

MC 5403

Joey Lakerdas-Gayle, University of Waterloo

Symmetrically indivisible and elementarily indivisible structures

A first order structure M is indivisible if for every colouring of M into two colours, there is a monochromatic substructure N of M that is isomorphic to M. We will consider two stronger properties: M is symmetrically indivisible if N can be chosen so that every automorphism of N extends to an automorphism of M; and M is elementarily indivisible if N can be chosen to be an elementary substructure of M. We will discuss Model-Theoretic methods developed by Kojman and Geschke (2008), Hasson, Kojman, and Onshuus (2009), and Meir (2019) to study the relationships between these notions.

MC 5403