Yang Hu (胡洋)

CV

This is my CV

I am interested in representation theory and its connections with number theory and algebraic geometry.

Abelian varieties over finite fields. Expository notes on Prof. Ananth Shankar’s lectures at the Arithmetic and Algebraic Geometry Bootcamp, Northwestern University, 2026. An introduction to abelian varieties over finite fields, emphasizing CM abelian varieties and Grothendieck–Messing deformation theory.
On Galois representations. Term paper for Number Theory (MATH 254A) at UC Berkeley, under the guidance of Prof. Sug Woo Shin, Fall 2025.
Abelian varieties and their moduli. Course notes from Prof. Kai-Wen Lan’s course.
Representation theory of reductive p-adic groups. Notes taken during Prof. Dihua Jiang’s topics course in spring 2026.
Notes on local theta correspondence. Expository notes from reading with Prof. Dihua Jiang.
A short note on surfaces of genus g. Expository notes on surface groups, period lattices, and the Abel–Jacobi map.
Period rings. Short wrap-up notes from the Berkeley Directed Reading Program, Fall 2025, on the construction of de Rham and crystalline period rings.
A note on an interesting Lemma

Finite-field Howe duality. An English translation generated with ChatGPT of Correspondance de Howe pour les groupes réductifs sur les corps finis.

Oscillator semigroups over finite fields: irreducible representations and restrictions. Working draft.

Motivated by Howe’s classification and restriction problems, we study the irreducible representations of centralizer semigroups in the oscillator semigroup over finite fields of odd characteristic, together with their restrictions to classical groups. We realize these restrictions as images of standard-module pairing operators and analyze them using Harish-Chandra induction and Hecke algebras of types A and BC. These constructions yield explicit restriction formulas and connect the semigroup representations with finite-field theta correspondence.
The oscillator semigroup approach to the Gurevich–Howe conjecture. In preparation.

This project develops an oscillator-semigroup approach to the Gurevich–Howe rank-agreement and exhaustion problems for finite symplectic groups. It compares the rank detected by Siegel unipotent characters with the smallest quadratic source in which a representation occurs in a Weil model. The draft identifies suitable corners of rank quotients of the symplectic group algebra with orthogonal group algebras, providing a route to rank agreement and exhaustion by the eta correspondence below maximal U-rank. It also relates semigroup defect to first occurrence in a fixed Witt tower.

Selected seminars, conferences, and summer schools attended.

Arithmetic and Algebraic Geometry Bootcamp. Northwestern University, Evanston, Illinois, August 17–21, 2026. Notes.
Summer Workshop on Character Sheaves on Loop Groups. Minneapolis, June 8–12, 2026.
Directed Reading Program, Fall 2025. UC Berkeley; mentored by CJ Dowd. Studied the construction of de Rham and crystalline period rings. Short wrap-up notes.
2025 CAS Summer School. Peking University. Lectures on algebraic geometry, number theory, and representation theory.
Learning Seminar on Fourier Analysis, Fall 2024. Southern University of Science and Technology. Presented Chapter 5 of Stein’s Fourier Analysis: An Introduction.