Events

Julius Frizzell, University of Waterloo

Multiple recurrence for weakly-mixing transformations.

We will cover some basic facts about weakly mixing transformations and work towards proving a version of the multiple recurrence theorem for measure-preserving systems with all of the transformations being weakly mixing.

MC 5417

Izar Alonso, Rutgers University

Gauge Theory on hyperkähler manifolds

$H$-instantons are a distinguished type of connections on Riemannian $n$-manifolds, as they are generalizations of anti-self-dual connections to manifolds of dimensions greater than 4. Examples of $H$-instantons include primitive Hermitian Yang--Mills (pHYM) connections, $\mathrm{Spin}(7)$-instantons,which have been of great interest in the recent years, and the less studied $\mathrm{Sp}(n)$-instantons. In this talk, I will describe $\mathrm{Sp}(2)$-instantons on hyperk\"ahler $8$-manifolds and their relations with other gauge-theoretical objects. I will then describe the construction of examples of $\mathrm{Sp}(2)$-instantons,pHYM connections, and $\mathrm{Spin}(7)$-instantons with symmetry on the manifold $T^* \mathbb{CP}^2$with the Calabi hyperk\"ahler structure. This talk is based on arXiv:2508.17119.

MC 5417

Ragini Singhal, University of Münster

Solutions and singularities of the Ricci-harmonic flow and Ricci-like flows of G2-structures

We find explicit solutions and singularities of the Ricci-harmonic flow of $G_2$-structures on 7-dimensionalcontact Calabi-Yau manifolds and the 7-dimensional Heisenberg group. We prove that the natural co-closed$G_2$-structure on a contact Calabi-Yau manifold as the initial condition leads to an ancient solution of the Ricci-harmonic flow with a finite time Type I singularity. These are the first examples of Type I singularities of the Ricci-harmonic flow. We also obtain similar (but different) results for the Ricci-like flows of $G_2$-structures studied by Gianniotis--Zacharopoulos in arXiv:2505.06872 (J. Geom. Anal. 36.2 (2026)) and of the negative gradient flow of an energy functional of $G_2$-structures studied by Weiss--Witt. The talk is based on a joint work with Shubham Dwivedi (Hamburg).

MC 5417

Joey Lakerdas-Gayle, University of Waterloo

Priority Arguments on Trees

We will introduce terminology for priority trees following Steffen Lempp's notes and compare the classicalpriority argument for Sacks Cone Avoidance Theorem with a proof that uses a priority tree.

MC 5403

Adina Goldberg, Mittag-Leffler Institute

Quantum games and quantum graphs via the double category of quantum relations

Binary relations are ubiquitous. Classical nonlocal games (Bell scenarios) can be thought of as binary relations between question pairs and answer pairs. Classical undirected graphs can be thought of as symmetric binary relations on a vertex set. There is a notion of quantum relation: a quantum analogue of binary relation. Just as relations can be transformed by functions, quantum relations can be transformed by quantum functions. The interactions between quantum relations and quantum functions are made precise by the double category of quantum sets, quantum functions, and quantum relations. We define this new double category building on the work of Weaver, Kornell, and Musto-Reutter-Verdon. We illustrate how the category suggests, distinguishes, and motivates quantizations of some constructions/results from classical graph theory and nonlocal games. Basicterms related to C*-algebras, bimodules, and category theory will come up, but the talk can also be followed by analogy to the classical setting.

QNC 1201

Julius Frizzell, University of Waterloo

Mutliple recurrence for weakly-mixing transformations (Part II)

We will continue to discuss weakly-mixing transformations and work towards proving a special case of the multiple recurrence theorem.

MC 5417