Stockholm

I will discuss the free compact boson CFT thrown out of equilibrium by marginal deformations, modeled by quenching or periodically driving the compactification radius of the free boson between two different values. All the dynamics will be shown to be crucially dependent on the ratio of the compactification radii via the Zamolodchikov distance in the space of marginal deformations. I will present various exact analytic results for the Loschmidt echo and the time evolution of energy density for both the quench and the periodic drive. Finally, I will present a non-perturbative computation of the  Rényi divergence, an information-theoretic distance measure, between two marginally deformed thermal density matrices.

The talk will be based on the recent preprint: arXiv:2206.11287

Some natural moduli problems give rise to stacks with infinite stabilizers. I will report on recent work with Dan Edidin where we give a canonical sequence of saturated blow-ups that makes the stabilizers finite. This generalizes earlier work in GIT by Kirwan and Reichstein, and on toric stacks by Edidin-More. Time permitting, I will also mention a recent application to generalized Donaldson-Thomas invariants by Kiem-Li-Savvas.

Linear operators preserving non-vanishing properties are an important

tool in e.g. combinatorics, the Lee-Yang program on phase transitions, complex analysis, matrix theory. We characterize all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing when the variables are in prescribed open circular domains, which solves the higher dimensional counterpart of a long-standing classification problem going back to P\'olya-Schur. This also leads to a self-contained theory of multivariate stable polynomials and a natural framework for dealing with Lee-Yang and Heilmann-Lieb type problems in a uniform manner. The talk is based on joint work with Petter Brändén.