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Virtual Workshop on Recent Developments in Geometric Representation Theory

Institute for Advanced Study via YouTube

Overview

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Explore cutting-edge developments in geometric representation theory through this comprehensive virtual workshop featuring 18 specialized lectures from leading mathematicians. Delve into advanced topics including theta intertwining sheaves, modular perverse sheaves on affine flag varieties, and the geometric Satake equivalence in mixed characteristic. Examine coherent categorification of quantum loop algebras, Picard groups of stable module categories, and path isomorphisms between quiver Hecke and diagrammatic Bott-Samelson endomorphisms. Investigate the center of small quantum groups, 2-Verma modules, and representations on KU-modules while analyzing stability and periodicity in modular representation theory. Study generalized affine Grassmannian slices, truncated shifted Yangians, and Hamiltonian structures alongside induction of p-cells and localization techniques. Learn about unitriangularity and decomposition matrices of unipotent blocks, reverse plane partitions and modules for preprojective algebras, and Macdonald polynomials with decomposition numbers for finite unitary groups. Discover real and symmetric Springer theory, curved Hecke categories, and perverse sheaves on configuration spaces with applications to Hopf algebras and parabolic induction, providing a comprehensive overview of current research directions in this rapidly evolving mathematical field.

Syllabus

Theta intertwining sheaves - Zhiwei Yun
Modular Perverse Sheaves on the affine Flag Variety - Laura Rider
The integral coefficient geometric Satake equivalence in mixed characteristic - Jize Yu
Coherent categorification of quantum loop sl(2) - Peng Shan
The Picard group of the stable module category of a finite group - Jesper Grodal
Path isomorphisms between quiver Hecke and diagrammatic Bott-Samelson endomorphism... - Amit Hazi
The center of the small quantum group - Pablo Boixeda Alvarez
2-Verma modules - Gregoire Naisse; Pedro Vaz
Representations on KU-modules - David Treumann
Stability and Periodicity in Modular Representation Theory - Nate Harman
Generalized affine Grassmannian slices, truncated shifted Yangians, Hamiltonian... - Joel Kamnitzer
Induction of p-Cells and Localization - Lars Thorge Jensen
Unitriangularity and Decomposition Matrices of Unipotent Blocks - Jay Taylor
Reverse Plane Partitions and Modules for the Preprojective Algebra - Anne Dranowski
Macdonald polynomials and decomposition numbers for finite unitary groups - Olivier Dudas
Real and symmetric Springer theory - David Nadler
Curved Hecke categories - Shotaro Makusumi
Perverse sheaves on configuration spaces, Hopf algebras and parabolic induction - Mikhail Kapranov

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Institute for Advanced Study

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