Andrei Okounkov (UCB) “The Eisenstein spectrum and some other things”
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
Henry Liu (Oxford) “Multiplicative vertex algebras and wall-crossing in equivariant K-theory”
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
Robert Lipshitz (UCB) “Floer homology for 3-manifolds with boundary”
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
Ivan Smith (Cambridge) “Annular symplectic Khovanov cohomology”
Abstract: I will discuss a symplectic version of annular Khovanov homology, taking place in Fukaya-Seidel categories of `horizontal’ Hilbert schemes of type A Milnor fibres. This talk reports on joint work with Cheuk Yu Mak.
Sergei Gukov (Caltech) “New developments in Vafa-Witten theory”
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
Tom Faulkner (UIUC) “Asymptotically Isometric Codes”
Abstract: “I review a class of quantum error correcting codes that directly takes into account the large-N aspects of holographic theories. I will discuss some aspects of the vacuum sector of these codes and use them to show the equivalence between two different approaches to entanglement wedge reconstruction.”
Yasha Neiman (OIST) “Locality of higher-spin gravity in de Sitter vs. in AdS”
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