Past Events
The $\hat{Z}$-invariants of three-manifolds introduced by Gukov, Pei, Putrov, and Vafa have influenced many areas of mathematics and physics. However, their TQFT structure is not yet fully understood. In this talk, I will present a framework for decorated Spin-TQFTs and construct one based on…
Physical dynamical systems amount to placing vector fields on manifolds. Important examples are noncanonical Hamiltonian systems, i.e., where the manifold is a Poisson manifold and the vector field is generated by a Hamiltonian function and a degenerate Poisson bracket. Physical systems…
Exponential last passage percolation (LPP) is a canonical planar directed model of random geometry in the KPZ universality class where the Euclidean metric is distorted by i.i.d. noise. One can also consider a dynamical version of LPP, where the noise is resampled at a constant rate, thereby…
Let K/Qp be a finite unramified extension and r a crystalline representation of G_K. The problem of finding all possibilities for the mod p reduction of r goes back to Serre. I will report on recent work with Bhargav Bhatt and Toby Gee, where we use prismatization to obtain some new…
We will continue our study of the lace expansion and its applications.
- Bergman Lecture
Act I: Convexity, Duality, and Volume
Once convexity, duality and volume appear on stage, the Mahler Conjectures are inevitable. These conjectures predict the extremizers of the volume of a convex body times the volume of its dual. They date from the 1930's and are still…
A graph is chordal if each of its cycles of length at least four has a chord. Chordal graphs occupy an extreme end of a trade-off between structure and generalization: they have strong structure and admit many interesting characterizations, but this strong structure makes them a…
I will discuss the existence and regularity of critical points of the area functional among Lagrangian surfaces in symplectic 4-manifolds, reviewing classical results by R. Schoen and J. Wolfson, as well as recent progress by A. Pigati and T. Rivière. I will then present a variational…