Wenhan Dai

Lectures on mod p Langlands program for GL(2)

Advanced guest lecture series.

This lecture series aims to give an introduction to some recent progress on the mod p Langlands program for GL(2).

• Lecturer: Yongquan Hu (MCM, AMSS).
• Other Invited Participants: Yiwen Ding, Ruochuan Liu, Yichao Tian, Haoran Wang, Liang Xiao, etc..
• Time: November 2 - November 16, 2022.
• Venue: Lecture Hall, 82J12, Jingchunyuan 82, BICMR.

Caveat: This series of courses contains a great deal of difficult and profound representational expertise that an audience unfamiliar with the field will not gain from.

Relevant Link

You are suggested to concern about this talk by Christophe Breuil (CNRS-Orsay) immediately following the course.

Syllabus

• (11/2) Lecture 1: Serre weights and Breuil-Paskunas’ construction. (notes)
• (11/9) Lecture 2: Gelfand-Kirillov dimension of some representations of GL(2). (notes)
• (11/16) (The lecture scheduled for this time has been cancelled due to force majeure.)
• (11/23) Lecture 3: Finite length results. (notes)
• (11/30) Lecture 4: Generalized Colmez’s functor. (notes)

References

1. C. Breuil, F. Herzig, Y. Hu, S. Morra, B. Schraen, Gelfand-Kirillov dimension and mod p cohomology for GL(2), arXiv: 2009.03127.
2. C. Breuil, F. Herzig, Y. Hu, S. Morra, B. Schraen, Conjectures and results on mod p representations of GL(n) for a p-adic field K, arXiv: 2102.06188.
3. C. Breuil, V. Paskunas, Towards a mod p Langlands correspondence for GL(2), Memoirs of AMS 216 (2012).
4. M. Emerton, T. Gee, D. Savitt, Lattices in the cohomology of Shimura curves, Invent. Math. 200 (2015).
5. Y. Hu, H. Wang, On the mod p cohomology for GL(2): the non-semisimple case, Cambridge J. Math 10 (2022).