PIRSA:C20030 - Geometric Representation TheoryPODCAST Subscribe to podcast

Geometric Representation Theory

Organizer(s): Andre Henriques   Joel Kamnitzer   Aaron Mazel-Gee   Ben Webster   Kevin McGerty   Catharina Stroppel   Carl Mautner   Tobias Barthe  

Collection URL: http://pirsa.org/C20030

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PIRSA:20060041  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Elliptic stable envelopes via loop spaces
Speaker(s): Michael McBreen
Abstract: Elliptic stable envelopes, introduced by Aganagic and Okounkov, are a key ingredient in the study of quantum integrable systems attached to a symplectic resolution. I will describe a relation between elliptic stable envelopes on a hypertoric variety and a certain 'loop space' of that variety. Joint ... read more
Date: 24/06/2020 - 10:00 am

PIRSA:20060031  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Global Demazure modules
Speaker(s): Michael Finkelberg
Abstract: The Beilinson-Drinfeld Grassmannian of a simple complex algebraic group admits a natural stratification into "global spherical Schubert varieties". In the case when the underlying curve is the affine line, we determine algebraically the global sections of the determinant line bundle over these globa... read more
Date: 24/06/2020 - 10:45 am

PIRSA:20060029  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Modular representations and perverse sheaves on affine flag varieties
Abstract: I will give an overview of a joint project with Simon Riche and Laura Rider and another one with Dima Arinkin aimed at a modular version of the equivalence between two geometric realization of the affine Hecke algebra and derived Satake equivalence respectively. As a byproduct we obtain a proof of t... read more
Date: 24/06/2020 - 12:00 pm

PIRSA:20060033  ( MP4 Medium Res , MP3 , PDF ) Which Format?
The ``Springer" representation of the DAHA
Speaker(s): Monica Vazirani
Abstract: The Springer resolution and resulting Springer sheaf are key players in geometric representation theory. While one can construct the Springer sheaf geometrically, Hotta and Kashiwara gave it a purely algebraic reincarnation in the language of equivariant $D(mathfrak{g})$-modules. For $G = GL_N$, the... read more
Date: 24/06/2020 - 2:00 pm

PIRSA:20060042  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Geometric class field theory and Cartier duality
Speaker(s): Justin Campbell
Abstract: I will explain a generalized Albanese property for smooth curves, which implies Deligne's geometric class field theory with arbitrary ramification. The proof essentially reduces to some well-known Cartier duality statements. This is joint work with Andreas Hayash.
Date: 24/06/2020 - 3:15 pm

PIRSA:20060045  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Relative critical loci, quiver moduli, and new lagrangian subvarieties
Speaker(s): Tristan Bozec
Abstract: The preprojective algebra of a quiver naturally appears when computing the cotangent to the quiver moduli, via the moment map. When considering the derived setting, it is replaced by its differential graded (dg) variant, introduced by Ginzburg. This construction can be generalized using potentia... read more
Date: 25/06/2020 - 11:15 am

PIRSA:20060034  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Parabolic restriction for Harish-Chandra bimodules and dynamical R-matrices
Speaker(s): Pavel Safronov
Abstract: The category of Harish-Chandra bimodules is ubiquitous in representation theory. In this talk I will explain their relationship to the theory of dynamical R-matrices (going back to the works of Donin and Mudrov) and quantum moment maps. I will also relate the monoidal properties of the parabolic res... read more
Date: 25/06/2020 - 12:00 pm

PIRSA:20060035  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Parabolic Hilbert schemes via the Dunkl-Opdam subalgebra
Speaker(s): Eugene Gorsky
Abstract: In this note we give an alternative presentation of the rational Cherednik algebra H_c corresponding to the permutation representation of S_n. As an application, we give an explicit combinatorial basis for all standard and simple modules if the denominator of c is at least n, and describe the ac... read more
Date: 25/06/2020 - 2:00 pm

PIRSA:20060046  ( MP4 Medium Res , MP3 , PDF ) Which Format?
An extension of Suzuki's functor to the critical level
Abstract: Suzuki's functor relates the representation theory of the affine Lie algebra to the representation theory of the rational Cherednik algebra in type A. In this talk, we discuss an extension of this functor to the critical level, t=0 case. This case is special because the respective categories of repr... read more
Date: 25/06/2020 - 3:15 pm

PIRSA:20060047  ( MP4 Medium Res , MP3 , PDF ) Which Format?
A categorification of the Lusztig—Vogan module
Speaker(s): Anna Romanov
Abstract: Admissible representations of real reductive Lie groups are a key player in the world of unitary representation theory. The characters of irreducible admissible representations were described by Lustig—Vogan in the 80’s in terms of a geometrically-defined module over the associated Hecke algebra... read more
Date: 25/06/2020 - 4:00 pm

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