Recurrence is central in ergodic Ramsey theory, and its multiplicative analogue is only now emerging. In this talk, I will define multiplicative recurrence, give illustrative examples, and explain how pretentious number theory is applied to establish it.

Zigzag persistence enables tracking topological changes in time-dependent data such as video streams. Nevertheless, traditional methods face severe computational and memory bottlenecks. In this talk, I show how the zigzag persistence of image sequences can be reduced to a graph problem, making it possible to leverage the near-linear time algorithm of Dey and Hou. By invoking Alexander duality, we obtain both H₀ and H₁ at the same computational cost, enabling fast computation of homological features. This speed-up brings us close to real-time analysis of dynamical systems, and, if time permits, I will outline how it opens the door to new applications such as the study of PDE dynamics using zigzag persistence, with the Gray-Scott diffusion equation as a motivating example.

theories on the lattice based on symmetry disentanglers: constant-depth
circuits of local unitaries that transform not-on-site symmetries into on-
site ones. When chiral symmetry can be realized not-on-site and such a
disentangler exists, the symmetry can be implemented in a strictly local
Hamiltonian and gauged by standard lattice methods. Using lattice ro-
tor models, we realize this idea in 1+1 and 3+1 spacetime dimensions
for U (1) symmetries with mixed ’t Hooft anomalies, and show that sym-
metry disentanglers can be constructed when anomalies cancel. As an
example, we present an exactly solvable Hamiltonian lattice model of the
(1+1)-dimensional “3450” chiral gauge theory, and we argue that a related
construction applies to the U (1) hypercharge symmetry of the Standard
Model fermions in 3+1 dimensions. Our results open a new route toward
fully local, nonperturbative formulations of chiral gauge theories.

Hamilton’s Ricci flow is a widely studied tool of geometric analysis, with a variety of applications. It is sometimes possible to obtain existence results for Ricci flows coming out of singular spaces, which leads to the question of uniqueness in these cases. In this talk, we will discuss a new result on uniqueness of Ricci flows coming out of Reifenberg Alexandrov spaces, and give some indication of the methods used in the proof.