An integral formula for dimensions of multiplicity spaces
Abstract. We explain how to compute the dimensions of certain multiplicity spaces between compact Lie groups using a relative trace formula argument.
About
Hi! I'm currently a Masters student at Johns Hopkins University studying robotics. Previously, I studied math and physics at UC Berkeley, where I was advised by Sug Woo Shin. I'm interested in algebraic number theory and its connections with algebraic geometry and representation theory. Specifically, I am interested in the geometry and cohomology of (local and global) Shimura varieties, and more generally moduli spaces of (local and global) shtukas. I am also interested in various topics in the intersection of robotics, machine learning, and computer vision, specifically in intelligent robot motion.
Email: my first name + my last initial @ berkeley dot edu
Research and Writing
GAGA For Varieties Over the Fargues-Fontaine Curve. Preprint (2026).
Blog
Click a post to show/hide its abstract.Talks
- October 2026, Student Number Theory Seminar. Restriction Problems and the GGP Conjectures.
- February 2026, Student Number Theory Seminar. The Gross–Zagier Formula I: Number Fields.
- February 2026, Student Number Theory Seminar. The Gross–Zagier Formula II: Function Fields.
- December 2025. Derived Categories and Algebraic Curves.
- December 2025, UC Berkeley Student Number Theory Seminar. p-adic Hodge Theory and Hodge–Tate Decompositions.
- May 2025. Completed Homological Stability for Sp₂ₙ.
- April 2025, UC Berkeley Student Automorphic Forms Seminar. The Local Langlands Correspondence and ℓ-adic Representations.
Teaching
Click a course to show/hide its description.Fall 2026: Instructor for Math 174, Introduction to Category Theory.
Student-led course. Covers categories, functors, natural transformations, universal properties, (co)limits, and adjunctions.
Fall 2026: Reader for Math 126, Introduction to PDEs.
An introduction to equations describing waves and diffusion, with initial and boundary conditions. Topics include Fourier methods, Green’s functions, maximum principles, and estimates for solutions.
Fall 2026: Reader for Math 121A, Math Methods for Physical Sciences.
Mathematical methods for students in the physical sciences, covering series, partial derivatives, complex analysis, integral transforms, and variational calculus.
Spring 2026: T.A for Math 254b, Algebraic Number Theory II.
Graduate course. Statements and proofs of (local and global) class field theory, complex multiplication of elliptic curves
Spring 2026: T.A for Math 256b, Algebraic Geometry II.
Graduate course. Sheaf cohomology, divisors, intersection theory, curves and surfaces.
Fall 2025: T.A for Math 256a, Algebraic Geometry I.
Graduate course. Sheaves, schemes, morphisms of schemes, sheaf cohomology.
Fall 2025, Spring 2025, Fall 2024: Lead Instructor for Math 174, Introduction to Category Theory.
Student-led course. Covers categories, functors, natural transformations, universal properties, (co)limits, and adjunctions.