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Home » Soergel Bimodules

Summer Graduate School

Soergel Bimodules June 26, 2017 - July 07, 2017
Parent Program: --
Location: MSRI: Simons Auditorium, Commons Room
Organizers LEAD Ben Elias (University of Oregon), Geordie Williamson (University of Sydney)
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     Group Photo
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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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Schedule
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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