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Summer Graduate School

Soergel Bimodules June 26, 2017 - July 07, 2017
Location: MSRI: Simons Auditorium, Commons Room
Organizers LEAD Benjamin Elias (University of Oregon), Geordie Williamson (Max-Planck-Institut für Mathematik)
Lecturer(s)

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Description

We will give an introduction to categorical representation theory, focusing on the example of Soergel bimodules, which is a categorification of the Iwahori-Hecke algebra. We will give a comprehensive introduction to the "tool box" of modern (higher) representation theory: diagrammatics, homotopy categories, categorical diagonalization, module categories, Drinfeld center, algebraic Hodge theory.

Suggested prerequisites:

  • Basic algebra topics: modules, bimodules, tensor product, linear algebra (bilinear forms, etcetera)
  • Basic homological algebra topics: Ext, projective objects, the homotopy and derived category, the Grothendieck group
  • Basic category theory topics: isomorphisms of functors, adjunctions.
Advantageous but not necessary:
 
  • Familiarity with complex semi-simple Lie algebras (root systems, Weyl groups, Coxeter groups).
  • Some familiarity with cohomology (long exact sequence of cohomology, cohomology of simple spaces like projective spaces, the circle etc).
  • Some familiarity with algebraic geometry (proper maps, the fibres of a morphism of varieties).
For eligibility and how to apply, see the Summer Graduate Schools homepage
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Tags/Keywords
  • Soergel bimodules

  • Hecke algebras

  • Coxeter groups

  • braid groups

  • Kazhdan-Lusztig conjecture

  • category O

  • hard Lefschetz

  • Hodge-Riemann bilinear relations

  • diagrammatics

  • categorification

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Secondary Mathematics Subject Classification
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