We study a prototypical geometric wave equation, given by wave maps from the Minkowski space R 1+d into the sphere S d , under the influence of additive stochastic forcing, in all energy-supercritical dimensions d ≥ 3. In the deterministic setting, self-similar finite-time blowup is expected for large data, but remains open beyond perturbative regimes. We show that adding a non-degenerate Gaussian noise provokes finite-time blowup with positive probability for arbitrary initial data. Moreover, the blowup is governed by the explicit self-similar profile originally identified in the deterministic theory. Our approach combines local well-posedness for stochastic wave equations, a Da Prato-Debussche decomposition, and a stability analysis in self-similar variables. The result corroborates the conjecture that the self-similar blowup mechanism is robust and represents the generic large-data behavior in the deterministic problem.

This is joint work with M. Hofmanova and E. Luongo (Bielefeld)

We discuss key results and milestones achieved while studying certain families of Diophantine equations as well as touching on open problems. We note that this is an overview of a large body of work involving multiple collaborators, including: A. Argáez-García (UADY), M. Bennett (UBC), N. Coppola (Padova), M. Curcó-Iranzo (Utrecht), S. Siksek (Warwick), M. Khawaja (Warwick) and Ö. Ülkem (Academia Sinica).

A d-dimensional TQFT is a topological invariant which assigns (d-1)-dimensional manifolds to vector spaces and d-dimensional cobordisms to linear maps. In the early 90s, Reshetikhin and Turaev constructed examples of these in the case d=3, using the data of certain types of linear categories. In this talk, I will provide an overview of this construction, and then explore how this might be meaningfully extended downwards to assign 1-manifolds to "2-vector spaces". Minimal knowledge of category theory assumed!