I will introduce the basic themes of the seminar: a) Hecke algebras and Kazhdan-Lusztig bases; b) Soergel bimodules; c) category \( O \) and the Kazhdan-Lusztig problem; and d) Soergel's categorification theorem and its implications.
The aim of this working group is to study the theory of Soergel bimodules and recent advances in diagrammatic categorification of Hecke algebras. The talks are all online and will be about 1 hour long, followed by a small discussion session for those interested. If you are interested in joining, please send an email to patnaik at ualberta dot ca .
The zoom link for the seminar is emailed to all participants.
The times listed below will be Edmonton time (E), Saskatoon time (S), Glasgow time (G), Hong Kong time (HK), and Pohang time (SK). The chapters indicated refer to the seminar's `offical' text Introduction to Soergel Bimodules.
| Date | Times | Speaker | Title and Abstract | Notes |
|---|---|---|---|---|
| October 6, 2023 | 7 AM (E,S), 2 PM (G) 9PM (HK), 10PM (SK) |
Manish Patnaik | I will introduce the basic themes of the seminar: a) Hecke algebras and Kazhdan-Lusztig bases; b) Soergel bimodules; c) category \( O \) and the Kazhdan-Lusztig problem; and d) Soergel's categorification theorem and its implications. |
|
| October 13, 2023 | 7 AM (E,S), 2 PM (G) 9PM (HK), 10PM (SK) |
Manish Patnaik | I will continue where I left off last time and discuss c) category \( O \) and the Kazhdan-Lusztig problem; and d) Soergel's conjecture and how it implies the Kazhdan-Lusztig theorem. |
|
| October 20, 2023 | 7 AM (E,S), 2 PM (G) 9PM (HK), 10PM (SK) |
Valentin Buciumas | We will discuss the "classical" theory of Seorgel bimodules in more detail, with a focus on examples. |
|
| October 27, 2023 | 7 AM (E,S), 2 PM (G) 9PM (HK), 10PM (SK) |
Valentin Buciumas | We'll discuss Soergel's categorification theorem and Soergel's conjecture in more detail, along with some examples, which ultimately motivate the diagrammatics in Part II of the book. |
|
| November 3, 2023 | 7 AM (E, S), 1 PM (G), 9PM (HK), 10PM (SK) | Yanze Chen | We will overview Soergel’s approach to the Kazhdan-Lusztig conjecture. After briefly introducing the category O for a semisimple Lie algebra, we will state the Kazhdan-Lusztig conjecture, and Soergel’s original approach using Soergel modules and the V-functor. |
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| Nov 10, 2023 | 7 AM (E), 8 AM (S), 2 PM (G), 10PM (HK), 11PM (SK) | Yanze Chen | We will continue to overview Soergel’s approach to the Kazhdan-Lusztig conjecture. After briefly introducing the category O for a semisimple Lie algebra, we will state the Kazhdan-Lusztig conjecture, and Soergel’s original approach using Soergel modules and the V-functor. |
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| Nov 17, 2023 | 7 AM (E), 8 AM (S), 2 PM (G), 10PM (HK), 11PM (SK) | Yanze Chen | We will continue to overview Soergel’s approach to the Kazhdan-Lusztig conjecture. After briefly introducing the category O for a semisimple Lie algebra, we will state the Kazhdan-Lusztig conjecture, and Soergel’s original approach using Soergel modules and the V-functor. |
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| Nov 24, 2023 | 7 AM (E), 8 AM (S), 2 PM (G), 10PM (HK), 11PM (SK) | Dinakar Muthiah | I'll briefly review constructible sheaves and explain how to categorify the Hecke algebra using equivariant sheaves on the flag variety. If there is time, I'll state and explain the monoidal equivalence between semi-simple complexes and Soergel bimodules. Otherwise, we'll start with this next week. Refs: Achar "Perverse Sheaves and Applications to Representation Theory" and L. Patimo's PhD thesis, available here |
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| Dec. 1, 2023 | 7 AM (E), 8 AM (S), 2 PM (G), 10PM (HK), 11PM (SK) | Dinakar Muthiah | Abstract here |
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| Dec. 8 2023 | 7 AM (E), 8 AM (S), 2 PM (G), 10PM (HK), 11PM (SK) | tba | Abstract here |
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| Dec. 15 2023 | 7 AM (E), 8 AM (S), 2 PM (G), 10PM (HK), 11PM (SK) | tba | Abstract here |
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| Dec. 22 2023 | 7 AM (E), 8 AM (S), 2 PM (G), 10PM (HK), 11PM (SK) | tba | Abstract here |