schedule

Schedule:

Wednesday 28 September

Clay Conference including Kevin Costello's talk and the prize award ceremony.

Thursday 29 September

10:00-11:00 Dan Freed

Title: A time-reversal anomaly, bordism, and index theory                                                                                                                                                      Abstract: I'll describe joint work with Mike Hopkins in which we prove an anomaly cancellation theorem in M-theory, an 11-dimensional flavor of string theory.  I assume no physics, so begin with a general discussion of anomalies and slowly close in on the problem at hand. The techniques used to solve the problem involve bordism computations, index theory, and the theory of cubic forms.

11:30-12:30 Claudia Scheimbauer

14:30-15:30 Soren Galatius

Title: Equivariant bordism categories and their classifying spaces                                                                                                                                            Abstract: To a small topological category C can be associated its classifying space BC, which retains some information about C but not everything (except when C is a groupoid, in which case C is equivalent to the fundamental groupoid of BC).  When C is the cobordism category whose objects are the closed smooth (d-1)-manifolds and whose morphisms are the compact d-dimensional cobordisms, it turned out that BC has an interesting and explicitly describable homotopy type.  I will discuss recent joint work with Szucs (arXiv:1805.12342) in which we give a similar description of the homotopy type of the classifying space of equivariant bordism categories.

16:00-17:00 Maxim Kontsevich

Title: Semi-infinite topology of Chern-Simons theory".

Abstract: Chern-Simons functional can be thought of as a cubic polynomial in infinitely many variables. I will explain how one can predict the monodromy structure on the "middle homology" of the complex level sets via resurgence of the quantum dilogarithm and counting of gradient trajectories of the classical dilogarithm. One can also see analogs of Hodge and weight filtrations in this "semi-infinite" limit of algebraic geometry

Friday 30 September

10:00-11:00 Oscar Randal-Williams

11:30-12:30 Constantin Teleman

14:30-15:30 David Ben-Zvi

Title: Higher geometric quantization and L-functionsAbstract: I'll describe a perspective on the theory of L-functions inspired by geometric quantization, developed in joint work with Yiannis Sakellaridis and Akshay Venkatesh. To a suitable class of hamiltonian actions of reductive groups one attaches two ``higher" quantization problems [in the sense of higher-dimensional QFT], one dubbed magnetic or automorphic and the other electric or spectral. Electric-magnetic / Langlands duality exchanges these quantization problems for dual reductive groups. I'll explain how, when considered in arithmetic contexts, the notion of automorphic quantization captures the theory of periods of automorphic forms, while spectral quantization captures the theory of L-functions of Galois representations. 

16:00-17:00 Mike Hopkins

Title:  The motivic Freudenthal suspension theorem                                                                                                                                                                    Abstract:  In topology, the Freudenthal suspension theorem connects the effective computational techniques in stable homotopy theory to problems of interest in ordinary homotopy theory.    The analogue of this result in the homotopy theory of smooth varieties (motivic homotopy theory) has been elusive. In this talk I will describe recent joint work with Aravind Asok and Tom Bachmann, establishing the motivic Freudenthal suspension theorem.   Time permitting I will survey some of the motivating and emerging applications.   

Dinner in honour of Graeme Segal

19:00 drinks

19:30 dinner

Merton College OX1 4JD