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:20060024  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Welcome and Opening Remarks
Speaker(s): Ben Webster
Date: 22/06/2020 - 10:15 am

PIRSA:20060028  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Singularities of Schubert varieties within a right cell
Speaker(s): Martina Lanini
Abstract: We describe an algorithm which takes as input any pair of permutations and gives as output two permutations lying in the same Kazhdan-Lusztig right cell. There is an isomorphism between the Richardson varieties corresponding to the two pairs of permutations which preserves the singularity type. ... read more
Date: 22/06/2020 - 10:45 am

PIRSA:20060026  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Yangians and cohomological Hall algebras of Higgs sheaves on curves
Speaker(s): Olivier Schiffmann
Abstract: We will review a set of conjectures related to the structure of cohomological Hall algebras (COHA) of categories of Higgs sheaves on curves. We then focus on the case of P^1, and relate its COHA to the affine Yangian of sl_2.
Date: 22/06/2020 - 12:00 pm

PIRSA:20060027  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Tate's thesis in the de Rham setting
Speaker(s): Sam Raskin
Abstract: This is joint work with Justin Hilburn. We will explain a theorem showing that D-modules on the Tate vector space of Laurent series are equivalent to ind-coherent sheaves on the space of rank 1 de Rham local systems on the punctured disc equipped with a flat section. Time permitting, we will also de... read more
Date: 22/06/2020 - 2:00 pm

PIRSA:20060038  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Fundamental local equivalences in quantum geometric Langlands
Speaker(s): Gurbir Dhillon
Abstract: In quantum geometric Langlands, the Satake equivalence plays a less prominent role than in the classical theory. Gaitsgory--Lurie proposed a conjectural substitute, later termed the fundamental local equivalence, relating categories of arc-integrable Kac--Moody representations and Whittaker D-module... read more
Date: 22/06/2020 - 3:15 pm

PIRSA:20060039  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Z-algebras from Coulomb branches
Speaker(s): Oscar Kivinen
Abstract: I will explain how to obtain the Gordon-Stafford construction and some related constructions of Z-algebras in the literature, using certain mathematical avatars of line defects in 3d N=4 theories. ‚ÄčTime permitting, I will discuss the K-theoretic and elliptic cases as well.
Date: 23/06/2020 - 10:00 am

PIRSA:20060025  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Cotangent complexes of moduli spaces and Ginzburg dg algebras
Speaker(s): Sarah Scherotzke
Abstract: We give an introduction to the notion of moduli stack of a dg category. We explain what shifted symplectic structures are and how they are connected to Calabi-Yau structures on dg categories. More concretely, we will show that the cotangent complex to the moduli stack of a dg category A admits a... read more
Date: 23/06/2020 - 10:45 am

PIRSA:20060032  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Centralizer of a regular unipotent element and perverse sheaves on the affine flag variety
Speaker(s): Laura Rider
Abstract: In this talk, I will give a geometric description of the category of representations of the centralizer of a regular unipotent element in a reductive algebraic group in terms of perverse sheaves on the Langlands dual affine flag variety. This is joint work with R. Bezrukavnikov and S. Riche.
Date: 23/06/2020 - 12:00 pm

PIRSA:20060030  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Type D quiver representation varieties, double Grassmannians, and symmetric varieties
Speaker(s): Jenna Rajchgot
Abstract: Since the 1980s, mathematicians have found connections between orbit closures in type A quiver representation varieties and Schubert varieties in type A flag varieties. For example, singularity types appearing in type A quiver orbit closures coincide with those appearing in Schubert varieties in typ... read more
Date: 23/06/2020 - 2:00 pm

PIRSA:20060040  ( MP4 Medium Res , MP3 , PDF ) Which Format?
K-theoretic Hall algebras for quivers with potential
Speaker(s): Tudor Padurariu
Abstract: Given a quiver with potential, Kontsevich-Soibelman constructed a Hall algebra on the cohomology of the stack of representations of (Q,W). In particular cases, one recovers positive parts of Yangians as defined by Maulik-Okounkov. For general (Q,W), the Hall algebra has nice structure properties, fo... read more
Date: 23/06/2020 - 3:15 pm

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