Home /  Soergel Bimodules

Summer Graduate School

Soergel Bimodules June 26, 2017 - July 07, 2017
Parent Program: --
Location: SLMath: Eisenbud Auditorium, Commons Room
Organizers LEAD Ben Elias (University of Oregon), Geordie Williamson (University of Sydney)
Lecturer(s)

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Teaching Assistants(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
 
 
Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords

  • Soergel bimodules

  • Hecke algebras

  • Coxeter groups

  • braid groups

  • Kazhdan-Lusztig conjecture

  • category O

  • hard Lefschetz

  • Hodge-Riemann bilinear relations

  • diagrammatics

  • categorification

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
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Schedule, Notes/Handouts & Videos
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Jun 26, 2017
Monday
09:15 AM - 09:30 AM
  Welcome
09:30 AM - 10:15 AM
  Lecture
10:15 AM - 10:45 AM
  Break
10:45 AM - 11:30 AM
  Lecture
11:30 AM - 12:30 PM
  Exercises
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:45 PM
  Lecture
02:45 PM - 03:15 PM
  Tea
03:15 PM - 05:00 PM
  Exercises and Discussion
Jun 27, 2017
Tuesday
09:30 AM - 10:15 AM
  Lecture
10:15 AM - 10:45 AM
  Break
10:45 AM - 11:30 AM
  Lecture
11:30 AM - 12:30 PM
  Exercises
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:45 PM
  Lecture
02:45 PM - 03:15 PM
  Tea
03:15 PM - 05:00 PM
  Exercises and Discussion
Jun 28, 2017
Wednesday
09:30 AM - 10:15 AM
  Lecture
10:15 AM - 10:45 AM
  Break
10:45 AM - 11:30 AM
  Lecture
11:30 AM - 12:00 PM
  Exercises
12:00 PM - 02:00 PM
  BBQ at Tilden Park
02:00 PM - 02:45 PM
  Lecture
02:45 PM - 03:15 PM
  Tea
03:15 PM - 05:00 PM
  Exercises and Discussion
Jun 29, 2017
Thursday
09:30 AM - 10:15 AM
  Lecture
10:15 AM - 10:45 AM
  Break
10:45 AM - 11:30 AM
  Lecture
11:30 AM - 12:30 PM
  Exercises
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:45 PM
  Lecture
02:45 PM - 03:15 PM
  Tea
03:15 PM - 05:00 PM
  Exercises and Discussion
Jun 30, 2017
Friday
09:30 AM - 10:15 AM
  Lecture
10:15 AM - 10:45 AM
  Break
10:45 AM - 11:30 AM
  Lecture
11:30 AM - 12:30 PM
  Exercises
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:45 PM
  Lecture
02:45 PM - 03:15 PM
  Tea
03:15 PM - 05:00 PM
  Exercises and Discussion
Jul 03, 2017
Monday
09:30 AM - 10:15 AM
  Lecture
10:15 AM - 10:45 AM
  Break
10:45 AM - 11:30 AM
  Lecture
11:30 AM - 12:30 PM
  Exercises
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:45 PM
  Lecture
02:45 PM - 03:15 PM
  Tea
03:15 PM - 05:00 PM
  Exercises and Discussion
Jul 05, 2017
Wednesday
09:30 AM - 10:15 AM
  Lecture
10:15 AM - 10:45 AM
  Break
10:45 AM - 11:30 AM
  Lecture
11:30 AM - 12:30 PM
  Exercises
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:45 PM
  Lecture
02:45 PM - 03:15 PM
  Tea
03:15 PM - 05:00 PM
  Exercises and Discussion
Jul 06, 2017
Thursday
09:30 AM - 10:15 AM
  Lecture
10:15 AM - 10:45 AM
  Break
10:45 AM - 11:30 AM
  Lecture
11:30 AM - 12:30 PM
  Exercises
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:45 PM
  Lecture
02:45 PM - 03:15 PM
  Tea
03:15 PM - 05:00 PM
  Exercises and Discussion
Jul 07, 2017
Friday
09:30 AM - 10:15 AM
  Lecture
10:15 AM - 10:45 AM
  Break
10:45 AM - 11:30 AM
  Lecture
11:30 AM - 12:30 PM
  Exercises
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:45 PM
  Lecture
02:45 PM - 03:15 PM
  Tea
03:15 PM - 05:00 PM
  Exercises and Discussion