Home /  Koszul Duality in the Local Langlands Program (St. Mary's College)

Summer Graduate School

Koszul Duality in the Local Langlands Program (St. Mary's College) July 01, 2024 - July 12, 2024
Parent Program: --
Location: St. Mary's College
Organizers Clifton Cunningham (University of Calgary), LEAD Sarah Dijols (University of British Columbia)
Lecturer(s)

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Teaching Assistants(s)

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Speaker(s)

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Description
2zul4skewl

This summer school provides the mathematical background to recognize Koszul duality in representation theory. The school is especially oriented toward applications in the local Langlands program, with an emphasis on real groups. As Koszul duality patterns have been initially observed in the context of Hecke algebras, our school will also introduce the students to Hecke algebras and their categorifications.

School Structure

There will be two courses, each of which will have multiple lectures, background sessions and problem sessions. There will also be ice-breaking activities, a hike and some evening sessions.

Bibliography

Prerequisites

A background in algebraic groups, representation theory and/or algebraic geometry (first graduate courses level) will be assumed.  No previous knowledge of Hecke algebras or Number Theory is expected.  In particular, the school is open to newcomers in the Langlands Program.  Students are expected to be familiar with most of the material in the classical introductory book of Humphreys “Introduction to Lie algebras and representation theory”, and to have read the first three chapters of Pramod Achar’s “Perverse sheaves and applications to representation theory” (errata).  The expectations make the school particularly suitable for PhD students in their second or later years of PhD.  Aspects form both of these textbooks will be reviewed in background sessions but at an accelerated pace. We should also mention that students may find additional resources on Pramod Achar’s webpage, in particular course notes, which might be slightly more introductory than his book.

We also recommend reading:

Application Procedure

For eligibility and how to apply, see the Summer Graduate Schools homepage.


 

Schedule, Notes/Handouts & Videos
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Jul 01, 2024
Monday
09:00 AM - 09:30 AM
  Welcome to the participants and intro to SLMath
09:30 AM - 11:30 AM
  Background Session (AG and RT)
Clifton Cunningham (University of Calgary), Sarah Dijols (University of British Columbia)
11:30 AM - 11:45 AM
  Break
11:45 AM - 12:15 PM
  Problem Session (AG and RT)
Clifton Cunningham (University of Calgary), Sarah Dijols (University of British Columbia)
12:15 PM - 01:45 PM
  Lunch
01:45 PM - 03:15 PM
  Problem Session, cont'd (AG and RT)
Clifton Cunningham (University of Calgary), Sarah Dijols (University of British Columbia)
03:15 PM - 03:45 PM
  Afternoon Tea
03:45 PM - 05:30 PM
  Introduction to Hecke algebras
Peng Shan (Tsinghua University)
Jul 02, 2024
Tuesday
09:15 AM - 10:45 AM
  Background Session (AG and RT)
Clifton Cunningham (University of Calgary), Sarah Dijols (University of British Columbia)
10:45 AM - 11:00 AM
  Break
11:00 AM - 12:30 PM
  Problem Session on Hecke algebras
12:30 PM - 01:45 PM
  Lunch
01:45 PM - 03:00 PM
  Second Lecture
Peng Shan (Tsinghua University)
03:00 PM - 03:30 PM
  Afternoon Tea
03:45 PM - 05:15 PM
  Problem Session
Clifton Cunningham (University of Calgary), Sarah Dijols (University of British Columbia)
Jul 03, 2024
Wednesday
09:15 AM - 10:45 AM
  First Lecture
Wolfgang Soergel (Albert-Ludwigs-Universität Freiburg)
10:45 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Ice-breaking activities (speed-networking)
12:00 PM - 01:45 PM
  BBQ Lunch
01:45 PM - 03:00 PM
  Problem Session
Clifton Cunningham (University of Calgary), Sarah Dijols (University of British Columbia)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 05:00 PM
  Geometry of Adam-Barbasch-Vogan for p-adic groups
Clifton Cunningham (University of Calgary)
Jul 04, 2024
Thursday
09:00 AM - 12:00 PM
  Free morning
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 04:00 PM
  Optional hike and social activities
Jul 05, 2024
Friday
09:15 AM - 10:30 AM
  Problem Session: "Geometry of ABV for p-adic groups"
Clifton Cunningham (University of Calgary)
10:30 AM - 10:45 AM
  Break
10:45 AM - 12:15 PM
  Second Lecture
Wolfgang Soergel (Albert-Ludwigs-Universität Freiburg)
12:15 PM - 01:45 PM
  Lunch
01:45 PM - 03:15 PM
  Third Lecture
Peng Shan (Tsinghua University)
03:15 PM - 03:45 PM
  Afternoon Tea
03:45 PM - 05:15 PM
  Problem Session
Clifton Cunningham (University of Calgary), Sarah Dijols (University of British Columbia)
05:30 PM - 08:00 PM
  Pub Social Event
Jul 08, 2024
Monday
09:15 AM - 10:30 AM
  Problem Session
Clifton Cunningham (University of Calgary), Sarah Dijols (University of British Columbia)
10:30 AM - 10:45 AM
  Break
10:45 AM - 12:15 PM
  Fourth lecture
Peng Shan (Tsinghua University)
12:15 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Third lecture
Wolfgang Soergel (Albert-Ludwigs-Universität Freiburg)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 05:30 PM
  Afternoon Break
Jul 09, 2024
Tuesday
09:15 AM - 10:30 AM
  Problem Session
Clifton Cunningham (University of Calgary), Sarah Dijols (University of British Columbia)
10:30 AM - 10:45 AM
  Break
10:45 AM - 12:15 PM
  Fifth Lecture
Peng Shan (Tsinghua University)
12:00 PM - 01:45 PM
  Lunch
01:45 PM - 03:00 PM
  Problem Session
Clifton Cunningham (University of Calgary), Sarah Dijols (University of British Columbia)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 05:30 PM
  Afternoon Break
05:30 PM - 07:00 PM
  Course-related examples from participants
Jul 10, 2024
Wednesday
09:15 AM - 10:45 AM
  Fourth Lecture
Wolfgang Soergel (Albert-Ludwigs-Universität Freiburg)
10:45 AM - 11:00 AM
  Break
11:00 AM - 12:15 PM
  Problem Session
Clifton Cunningham (University of Calgary), Sarah Dijols (University of British Columbia)
12:15 PM - 01:30 PM
  Lunch
01:30 PM - 01:45 PM
  Group Photo
01:45 PM - 03:00 PM
  Problem Session or additional time for a lecture, if needed
03:30 PM - 05:30 PM
  Afternoon Break
Jul 11, 2024
Thursday
09:30 AM - 11:00 AM
  Fifth Lecture
Wolfgang Soergel (Albert-Ludwigs-Universität Freiburg)
11:00 AM - 11:15 AM
  Break
11:15 AM - 12:15 PM
  Problem Session
Clifton Cunningham (University of Calgary), Sarah Dijols (University of British Columbia)
12:15 PM - 01:45 PM
  Lunch
02:00 PM - 04:30 PM
  Visit to SLMath
Jul 12, 2024
Friday
09:15 AM - 09:45 AM
  Participants' Survey
09:45 AM - 11:00 AM
  Sixth Lecture
Wolfgang Soergel (Albert-Ludwigs-Universität Freiburg)
11:00 AM - 11:15 AM
  Break
11:15 AM - 12:15 PM
  Problem Session
Clifton Cunningham (University of Calgary), Sarah Dijols (University of British Columbia)
12:15 PM - 02:00 PM
  Lunch
01:45 PM - 03:00 PM
  Final Discussion or Questions