Arithmetic Geometry Lab

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My research interests are primarily in the area of number theory. Specifically, I am interested in p-adic Galois representations and algebraic automorphic forms. I am currently working on a project that aims to giving an evidence towards mod-p Langlands program.
One formulation of a hypothetical mod-p local Langlands correspondence is the existence of an injection from the set of mod-p Galois representations to the set of mod-p admissible representations, which is compatible with global correspondence occurring in the mod-p cohomology of locally symmetric spaces. At present, the only known case of such a correspondence is GL_2(Q_p). For a given mod-p Galois representation, one can define a candidate of mod-p admissible representation for mod-p Langlands correspondence, via the global correspondence, and I am currently studying the structure of the candidate to see if it determines the given Galois representation.

Major research field

Galois representations, Integral p-adic Hodge theory, Automorphic representations

Desired field of research

Emerton--Gee Stacks, Local models

Research Keywords and Topics

- The weight part of Serre-type conjectures,
- The Breuil--Mezard conjectures,
- Mod-p/p-adic Langlands programs,
- Categorical p-adic Langlands program.

Research Publications

- On mod p local-global compatibility for GL_n(Q_p) in the ordinary case (with Zicheng Qian)
Les Memoires de la Societe Mathematique de France. 173 (2022) vi+150.
- On mod p local-global compatibility for GL_3(Q_p) in the non-ordinary case (with Daniel Le, Stefano Morra)
Proceedings of the London Mathematical Society 117 (2018) 790--848.
- Reduction modulo p of certain semi-stable representations
Transactions of the American Mathematical Society 369 (2017) 5425--5466.


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