SIYAN DANIEL LI-HUERTA


Picture of me in Taiwan.

Department of Mathematics

Harvard University

sli@math.harvard.edu

I am a third-year graduate student at Harvard University advised by Mark Kisin.

For a year, I was a graduate student at the University of Chicago. Before that, I was an undergraduate at Princeton University, where my senior thesis was advised by Sophie Morel.

RESEARCH

The plectic conjecture over function fields. (pdf) (arXiv)

Let Q be a global field of positive characteristic. We prove the plectic conjecture of Nekovář–Scholl for moduli spaces of shtukas over Q. For example, when the cocharacter is defined over Q and the structure group is a Weil restriction from a degree d separable extension F/Q with the same constant field, we construct an action of (Sd ltimes Weil(F)d)I on the ℓ-adic intersection cohomology with compact support of the associated moduli space of shtukas over QI. This extends the action of Weil(Q)I constructed by Xue along the I-fold product of the map Weil(Q) → Sd ltimes Weil(F)d. We show that the action of (Sd ltimes Weil(F)d)I commutes with the Hecke action, and we give a moduli-theoretic description of the action of Frobenius elements in Weil(F)d×I.

The local Langlands correspondence for GLn over function fields. (pdf) (arXiv)

Let F be a local field of characteristic p > 0. By adapting methods of Scholze, we give a new proof of the local Langlands correspondence for GLn over F. More specifically, we construct ℓ-adic Galois representations associated with many discrete automorphic representations over global function fields, which we use to construct a map π→rec(π) from isomorphism classes of irreducible smooth representations of GLn(F) to isomorphism classes of n-dimensional semisimple continuous representations of WF. Our map rec is characterized in terms of a local compatibility condition on traces of a certain test function fτ,h, and we prove that rec equals the usual local Langlands correspondence (after forgetting the monodromy operator).

TEACHING

Math 1a: Introduction to Calculus (Fall 2021)

Math 99r: Fourier Analysis on Number Fields (Fall 2020)

Math 1b: Calculus, Series, and Differential Equations (Fall 2019)