The local Langlands correspondence can be used as a tool for making verifiable predictions
about irreducible complex representations of p-adic groups and their Langlands parameters …

We introduce a new approach to the representation theory of reductive $ p $-adic groups $
G $, based on the geometric invariant theory (GIT) of Moy-Prasad quotients. Stable …

We study sums over primes of trace functions of ℓ-adic sheaves. Using an extension of our
earlier results on algebraic twists of modular forms to the case of Eisenstein series and …

We prove the (generalized) coherence conjecture proposed by Pappas and Rapoport. As a
corollary, one of their theorems, which describes the geometry of the special fibers of the …

The test function conjecture for parahoric local models Page 1 JOURNAL OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 34, Number 1, January 2021, Pages 135–218 …

The first part of this article is a review of the properties expected of any local Langlands
correspondence that aims to be considered" canonical," and of known results that establish …

We generalize the works of Pappas–Rapoport–Zhu on twisted affine Grassmannians to the
wildly ramified case under mild assumptions. This rests on a construction of certain smooth …

We construct motivic ℓ-adic representations of Gal(Q/Q) into exceptional groups of type E 7,
E 8 and G 2 whose image is Zariski dense. This answers a question of Serre. The …

Schubert varieties in classical flag varieties are known to be normal by the work of Ramanan-
Ramanathan, Seshadri, Anderson and Mehta-Srinivas. The normality of Schubert varieties …

For any simple algebraic group G of exceptional type, we construct geometric ℓ ℓ-adic Galois
representations with algebraic monodromy group equal to G, in particular producing the first …