Abstract: The spectral decomposition of the Hilbert space of automorphic functions is a very old and central topic in number theory, and mathematics in general. In particular, the Eisenstein series produce automorphic functions on a group G from automorphic functions on its Levi subgroups and one is interested in spectrally decomposing them. I will review some classical as well as … Read More

Abstract: I will explain how a recent “universal wall-crossing”framework of Joyce works in equivariant K-theory, which I view as amultiplicative refinement of equivariant cohomology. Enumerativeinvariants, possibly of strictly semistable objects living on the walls, are controlled by a certain (multiplicative version of) vertex lgebra structure on the K-homology groups of the ambient stack. In very special settings like refined Vafa-Witten … Read More

Ozsváth-Szabó’s Heegaard Floer homology is a holomorphic curve analogue of the Seiberg-Witten Floer homology of closed 3-manifolds. Bordered Heegaard Floer homology is an extension of (one version of) Heegaard Floer homology to 3-manifolds with boundary, developed jointly with Ozsváth and Thurston. This talk is an overview of bordered Heegaard Floer homology. We will start by describing the structure and aspects … Read More

Abstract: Many gauge theories in four dimensions are based on PDEs that involve a gauge connection coupled to other fields. The latter are usually a source of a major headache since they lead to non-compactness of the moduli spaces. Today we will discuss two aspects of this major problem and two ways of dealing with it. One will help us … Read More

Abstract: We consider higher-spin gravity in (A)dS_4, defined as the holographic dual of a free O(N) or Sp(N) vector model. At the quartic level, this theory has been judged non-local at distances greater than the (A)dS radius, due to a mismatch of massless (twist=1) exchange-type terms in its boundary OPE behavior. We review the non-locality argument, and note that it relies … Read More