Student Learning Seminar on the Langlands Program (Spring 2017)

Logistics

Time: 4:15 pm - 5:45 pm on Wednesdays
Location: 507 Mathematics
Dinner: Meet at 6 pm in the Mathematics Building Lobby

This semester Shizhang Li, Samuel Mundy and I are organizing a learning seminar on the Langlands program. The main goals are to understand the statements of the Langlands conjecture (over global and local fields) and the geometric Langlands conjecture, and to survey some of the known results.

Of relevance to this seminar is Michael Harris' topics course on the trace formula and p-adic L-functions, as well as the student algebraic geometry seminar (organized by Shizhang Li and Carl Lian) on perverse sheaves and the decomposition theorem.

Please email me if you would like to join the mailing list for this seminar.

Main References

Supplementary References

Schedule

The schedule is tentative and subject to change as the seminar moves along.

Note that Lecture 1 (January 18) took place in 622 Mathematics, but the seminar has since been moved to 507 Mathematics for the rest of the semester.

  Date  Speaker  Topic  References 
Lecture 1  January 18  Samuel Mundy  Tate's thesis  [Mun] 
Lecture 2  January 25  Pak-Hin Lee  Langlands for GL(1), and an overview of the Langlands conjectures   
Lecture 3  February 1  Qixiao Ma  Galois representations and L-functions  [BG, Ch. 4], [T, §1-2] 
Lecture 4  February 9
(Date change)
Samuel Mundy  Weil--Deligne representations, and compatible systems of Galois representations  [T, §1-2] 
Lecture 5  February 15  Yang An  From modular forms to automorphic representations  [BG, Ch. 7], [T, §3] 
Lecture 6  February 22  Samuel Mundy  Automorphic L-functions  [GH, Ch. 11] 
Lecture 7  March 1  Pak-Hin Lee  The global Langlands correspondence for GL(2)  [BG, Ch. 10], [Bum, Ch. 2], [C], [K] 
Lecture 8  March 9
(Date change)
Pak-Hin Lee  The local Langlands correspondence for GL(2) over R, and more on the global correspondence 
No talk  March 15    Spring Break   
Lecture 9  March 22  Qirui Li  The local Langlands correspondence for GL(2) over p-adic fields  [Buz] 
Lecture 10  March 29  Qirui Li  The local Langlands correspondence for GL(2) over p-adic fields (continued)  [Buz] 
David Hansen  Langlands functoriality: motivations and applications   
Lecture 11  April 7
(Date change)
Michael Harris  Special lecture: Counting points on compact Shimura varieties, and the trace formula 
(Location: 407 Mathematics)
 
Lecture 12  April 12  Shizhang Li  Algebraic theory of Drinfeld modules  [DH, Ch. 1], [Fl, Ch. 3-4] 
Lecture 13  April 19  Jingwei Xiao  Analytic theory of Drinfeld modules  [DH, Ch. 2] 
Lecture 14  April 26  Daniel Gulotta  Covering space of Drinfeld moduli spaces, and the correspondence between Drinfeld modules and shtukas  [DH, Ch. 3], [D2], [Mum], [Go, Ch. 6] 
Lecture 15  May 3  Shizhang Li  Cohomology of Drinfeld moduli spaces  [DH, Ch. 4] 
Lecture 16  May 10  Daniel Litt  Overview of Drinfeld's proof of the Langlands correspondence for GL(2) over function fields  [DH, Ch. 5], [D], [Fl] 

Last updated: April 19, 2017.

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