Geometric representation theory
Organized by: David Ben-Zvi, Roman Bezrukavnikov and Alexander Braverman
January 4-29th, 2016
The program will focus on emerging trends in representation theory and their relation to the more traditional ideas of the subject. The celebrated success of the perverse sheaves methods in 1980’s has led to development of a direction which may be called geometric categorification, where the primary object of study is a category of sheaves on an appropriate geometric space (stack): this includes theories of character sheaves, geometric Langlands duality, various approaches to categorification based on quiver varieties etc. Recently significant progress has been achieved in developing and systematizing these constructions and new algebraic methods inspired by D-modulesand perverse sheaves have been discovered. Other recent works indicate relation of this area to ideas of physical origin such as topological quantum field theory and wall-crossing, and their mathematical manifestations including cluster algebras, Bridgeland stabilities and quantum cohomology. The program will bring together experts in these different directions creating an opportunity for a synthesis of the diverse approaches and further progress.
All talks will be held in the SCGP Seminar Room, Rm 313.
|Loop Grassmannians, classifying spaces and local spaces
|Ivan Mirkovic (U.Mass. Amherst)
|Cohomological Hall algebras and affine quantum groups
|Yaping Yang (U. Mass. Amherst)
|Elliptic quantum groups
|Sachin Gautam (Perimeter Institute)
|Recent Developments in the Geometric Langlands Program
|Dima Arinkin (Wisconsin)
|Elliptic stable envelopes
|Andrei Okounkov (Columbia)
|Donaldson-Thomas transformations for moduli spaces of local systems on surfaces.
|Alexander Goncharov (Yale)
|Tilting modules and the p-canonical basis
|Geordie Williamson (Max Planck)
|Semiclassical Geometric Langlands Correspondence
|Dima Arinkin (Wisconsin)
|Applications of 3d N=4 theories in geometric representation theory
|Tudor Dimofte (Perimeter)
|BGG resolutions for rational Cherednik algebras
|Stephen Griffeth (Talca)
|Cherkis’ bow varieties and Coulomb branches of quiver gauge
theories of affine type A.
|Studying the decomposition theorem over the integers
|Quivers and qq-characters
*Also part of the Seminar Series “Mathematics and Physics of Calogero-Moser-Sutherland systems”
|On categories O for quantized symplectic resolutions
|An involution based left ideal in the Hecke algebra
|Miura bimodule, the affine Grassmannian, and nil-DAHA
|Towards a cluster structure on trigonometric zastava
|Homomorphisms between different quantum toroidal and affine Yangian algebras.
|Microlocal Sheaves and Cluster Algebras
|Perverse sheaves on arc spaces, central sheaves and local L-functions
(joint work with D.Kazhdan and R.Bezrukavnikov).