Lie Theory without Groups: Enumerative Geometry and Quantization of Symplectic Resolutions

YouTube playlist

Organizers:

David Kazhdan (The Hebrew University)
Andrei Okounkov (Columbia University)
Roman Bezrukavnikov (Massachusetts Institute of Technology)

Recently found answers to a number of questions in enumerative algebraic geometry are formulated in terms of highly nontrivial Lie theoretic structures. A prominent example is provided by calculation of quantum cohomology and quantum K-theory of some symplectic resolutions of singularities. On the other hand, quantizations of such resolutions form a natural generalization of enveloping algebras of semi-simple Lie algebras. Representation theory of these quantizations shows surprising connections to enumerative geometry of the resolution. It is also expected to be closely related to categorical invariants of the resolution studied in symplectic geometry, such as the Fukaya category. The goal of the workshop is to give an introduction to this circle of ideas and stimulate work towards conceptual understanding of the observed phenomena.

List of Speakers and Topics

NAME	TOPIC
Roman Bezrukavnikov (MIT)	Canonical Bases and Geometry
Anton Kapustin (Caltech)	Branes and quantizations
Maxim Kontsevich (IHES France)	Generalized Riemann-Hilbert Correspondence
Ivan Loseu (Northeastern University)	Quantizations of Nakajima Varieties
Davesh Maulik (MIT) & Andrei Okounkov (Columbia University)	Representation Theory and Enumerative Geometry
Jake Solomon (Hebrew University)	J-holomorphic Curves with I-holomorphic Lagrangian Boundary Conditions
Alexander Beilinson (University of Chicago)	Around the characteristic cycle
Dennis Gaitsgory (Harvard)	Metaplectic Whittaker category and quantum groups