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.