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 prosimplicial 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. 
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, §610, [Gee], [GV]§13, [T] 
March 4  Robin Zhang  Calegari—Geraghty method: Modularity lifting  [CG]§13, §5, [Ger] 
March 11  Yogesh More (Remote)  Derived deformation theory (Slides)  [GV]§4.34.6, 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  [GV]§4.64.7, §89, [B] 
April 8  Haodong Yao (Remote)  The derived deformation ring and patching  [GV]§1314, [CG]§2, §6, [I] 
April 15  — (Remote)  Derived Hecke algebra I  [V] 
April 22  — (Remote)  Derived Hecke algebra II  [V] 
April 29  — (Remote)  Derived Hecke algebra III  [V] 
May 6  — (Remote)  The derived deformation ring and derived Hecke algebra  [GV]§1, §15 
TBD  Eric Urban (Remote)  —  — 
References
Articles

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