Geometric representation theory: January 4-29th, 2016

Geometric representation theory

Organized by: David Ben-Zvi, Roman Bezrukavnikov and Alexander Braverman
January 4-29th, 2016

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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.

Date Time Title Speaker
1/5/2016 10:30am Loop Grassmannians, classifying spaces and local spaces Ivan Mirkovic (U.Mass. Amherst)
1/5/2016 2:30pm Cohomological Hall algebras and affine quantum groups Yaping Yang (U. Mass. Amherst)
1/7/2016 10:30am Elliptic quantum groups Sachin Gautam (Perimeter Institute)
1/7/2016 2:30pm Recent Developments in the Geometric Langlands Program Dima Arinkin (Wisconsin)
1/11/2016 2:30pm Elliptic stable envelopes Andrei Okounkov (Columbia)
1/12/2016 10:30am Donaldson-Thomas transformations for moduli spaces of local systems on surfaces. Alexander Goncharov (Yale)
1/12/2016 2:30pm Tilting modules and the p-canonical basis Geordie Williamson (Max Planck)
1/14/2016 10:30am Semiclassical Geometric Langlands Correspondence Dima Arinkin (Wisconsin)
1/14/2016 2:30pm Applications of 3d N=4 theories in geometric representation theory Tudor Dimofte (Perimeter)
1/15/2016 10:30am BGG resolutions for rational Cherednik algebras Stephen Griffeth (Talca)
 1/19/2016 10:30 am Cherkis’ bow varieties and Coulomb branches of quiver gauge
theories of affine type A.
Hiraku Nakajima
1/20/2016 10:30am Studying the decomposition theorem over the integers Geordie Williamson
1/20/2016 2:30pm Quivers and qq-characters

*Also part of the Seminar Series “Mathematics and Physics of Calogero-Moser-Sutherland systems”

Nikita Nekrasov
1/21/2016 10:30am On categories O for quantized symplectic resolutions Ivan Losev
1/22/2016 10:30am An involution based left ideal in the Hecke algebra George Lusztig
1/22/2016 10:30am Miura  bimodule, the affine Grassmannian, and nil-DAHA Victor Ginzburg
1/25/2016 10:30am  Towards a cluster structure on trigonometric zastava Michael Finkelberg
1/25/2016 2:30pm  Homomorphisms between different quantum toroidal and affine Yangian algebras. Oleksandr Tsymbalyuk
1/26/2015 10:30am Microlocal Sheaves and Cluster Algebras Harold Williams
1/27/2015 10:30am Perverse sheaves on arc spaces, central sheaves and local L-functions
(joint work with D.Kazhdan and R.Bezrukavnikov).
Alexander Braverman

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