Abstract: In this talk we will review past and recent results pertaining to the emerging field of integrable space-time nonlocal nonlinear evolution equations. In particular, we will discuss blow-up in finite time of soliton solutions as well as the physical derivations of many integrable nonlocal systems.

Abstract: We formulate the holomorphic twists of the 6d N=(0,1) and (0,2) abelian superconformal theories as moduli spaces in derived algebraic geometry, using Deligne cohomology as a key tool. This description allows one to mimic the Beilinson-Drinfeld construction of lattice chiral algebras to quantize these 6d theories; their factorization homology on a projective complex 3-fold X relates to Witten’s construction of line bundles on intermediate Jacobian of X. This is work in progress with Chris Elliott, Ingmar Saberi, and Brian Williams.