Robin Zhang | Columbia University



Student Number Theory Seminar

Derived Galois Deformation Rings

Spring 2020

This semester's edition of the Student Number Theory Seminar will focus on studying derived Galois deformation rings,
partially inspired by the 2017 Heidelberg Study Group/Forschungsseminar and the 2019 London Number Theory Study Group.

The goal is to follow the paper of Galatius—Venkatesh, define a pro-simplicial ring whose zeroth homotopy group is Mazur's Galois deformation ring, and
define a graded action of derived deformation rings on the homology of arithmetic groups in the sense of a hypothetical derived Langlands program.

Along the way, the seminar will provide a gentle introduction to the necessary homotopy theory and review the Taylor—Wiles method and its extensions.
The seminar meets from 4:30pm — 6:00pm, Wednesdays in Mathematics Room 507.
The talks will be followed by dinner.

The in-person seminar is indefinitely postponed due to the COVID-19 pandemic.
All talks after March 11 will be held remotely.
(Three "pre-seminar" talks from last semester are also listed here)
Date Speaker Title References
November 8 Michael Harris Organizational meeting
November 21 Ashwin Iyengar Galois deformation theory [St]
December 12 Sam Mundy The Taylor—Wiles method [Di]
February 5 Roy Magen Homotopy background I [LP], [GJ], [L1]§1.2.3, [R]
February 12 Inbar Klang Model categories
February 19 Michael Harris Simplicial rings [Ma], [W]§8, [F], [GV]§2, [Si]
February 26 Stanislav Atanasov Calegari—Geraghty method: General framework [CG]§1, §6-10, [Gee], [GV]§13, [T]
March 4 Robin Zhang Calegari—Geraghty method: Modularity lifting [CG]§1-3, §5, [Ger]
March 11 Yogesh More (Remote) Derived deformation theory (Slides) [GV]§4.3-4.6, Appendix A, [Da], [L2]§6.2
March 18 Spring Break (no talk) Spring Break (no talk) Spring Break
March 25 Cancelled (no talk) Cancelled (no talk) Cancelled
April 2 Hung Chiang (Remote) Simplicial Galois representations (Notes) [GV]§4.6-4.7, §8-9, [B]
April 8 Haodong Yao (Remote) The derived deformation ring and patching (Slides) [GV]§13-14, [CG]§2, §6, [I]
April 22 Stanislav Atanasov (Remote) Derived Hecke algebra I (Slides) [V]
May 6 Chi Dung Nguyen (Remote) Derived Hecke algebra II [V]
May 13 Michael Harris (Remote) Derived Hecke action at p and the ordinary Hida tower [KR]

References

Articles London Number Theory Study Group (Winter 2019) notes Textbooks, surveys, and other notes

Organizers: Stanislav Atanasov, Michael Harris, and Robin Zhang

<< Fall 2019