As part of the Arithmetic Geometry Learning Seminar, this semester we will have a joint seminar with IU-Bloomington on the theory of Condensed Mathematics due to Clausen-Scholze. The seminar will be live streamed over zoom with speakers alternating between IU and Purdue. We will also reserve a room locally at Purdue (for local speakers).
The seminar will culminate in a workshop during the last weekend of April where we plan to learn about Scholze's recent work on real local Langlands correspondence.
Time: Mondays, 2:30-3:55
Location: SCHM 309 (For Purdue participants)
Zoom Link: Please send one of the organizers an e-mail in order to be added to the group e-mail list and receive a zoom link.
The suggested topics and content for each talk is available here.
Talk 1 (Jan 13): Condensed sets (Zichuan Wang, IU) (Notes)
Talk 2 (Jan 27): Condensed abelian groups (Zichuan Wang, IU) (Notes)
Talk 3 (Feb 3): Cohomology (Linquan Ma, Purdue) (Notes)
Talk 4 (Feb 10): Analytic rings (Vladimir Shein, IU) (Notes)
Talk 5 (Feb 17): Locally compact abelian groups (Daniel Le, Purdue) (Notes)
Talk 6 (Feb 24): Solid abelian groups I (Heejong Lee, Purdue) (Notes)
Talk 7 (Mar 3): Solid abelian groups II (Donu Arapura, Purdue) (Notes)
Talk 8 (Mar 10): Condensed/M-complete R-vector spaces (Matthias Strauch, IU) (Notes)
Talk 9 (Mar 24): Liquid Vector Spaces (Matthias Strauch, IU) (Notes)
Talk 10 (Mar 31)): Analytic Rings Revisited (Vladimir Shein, IU) (Notes)
Talk 11 (Apr 7): Infinity Categories (Manuel Riviera, Purdue) (Notes)
Talk 12 (Apr 14): Analytic Stacks (Vladimir Shein, IU) (Notes)
Talk 13 (Apr 21): Complex Analytic Spaces (Deepam Patel, Purdue) (Notes)
Condensed Mathematics Workshop: April 26-27
Location: Engineering Technology 202 (ET 202)
Schedule
Saturday, April 26:
10:00 - 11:00 The classical Hirzebruch-Riemann-Roch Theorem (Donu Arapura)
coffee break
11:30 - 12:30 Hirzebruch-Riemann-Roch for complex analytic spaces I(Deepam Patel)
lunch break
2:00 - 3:00 Local Langlands and Jacquet-Langlands for real and p-adic GL(2) (Hyeonmin Cheon and Junoh Kim)
coffee break
3:45 - 4:45 Carayol's non-abelian Lubin-Tate theory (Matthias Strauch)
5:00-5:45: Career Panel (TBA)
6:00 dinner
Sunday, April 27:
9:30 - 10:30 Hirzebruch-Riemann-Roch for complex analytic spaces II (Deepam Patel)
coffee break
11:00 - 11:40: Local Langlands for GL(2,R) and analytic stacks 1 (Vladimir Shein)
11:45-12:30: Local Langlands for GL(2,R) and analytic stacks 2 (Matthias Strauch)
References:
[CS1] Lectures on Condensed Mathematics (Clausen-Scholze)
[CS2] Lectures on Analytic Geometry (Clausen-Scholze)
[CS3] Condensed Mathematics and Analytic Geometry (Clausen-Scholze)
[C] Notes on Condensed Math (Camargo)
[H] Descent for Sheaves on Compact Hausdorf Spaces (P. Haine)
[K] Notes from a course by Kedlaya available here.
[L] Condensed Mathematics (Master's Thesis) (Leptien)