Alan Goldfarb

Email: alangoldfarb [AT] berkeley [DOT] edu

1075 Evans Hall, University Dr
Berkeley, CA 94720 USA


About Me

I'm a third-year PhD candidate in the mathematics department at UC Berkeley fortunate to be advised by Vera Serganova.
My research interests are in the representation theory of quantum groups and superalgebras, often in the context of geometry, tensor categories, and mathematical physics.
Before coming to Berkeley and moving my focus to representation theory, I was a student of
Sarthak Parikh studying p-adic field theories at Caltech.
I was a Presidential Scholar at USC and received my B.S. in mathematics, summa cum laude, in 2023.

This semester, I'm organizing a seminar on quantum groups and affine Lie algebras. We meet every Tuesday at 2:00pm in Evans 939.
I co-organize our department's directed reading program. It is a great way for undergraduates to engage with research-level math and for graduate students to support math education.
I also organize our department's poker club and am an avid player. Feel free to reach out if interested.

Because I cannot ignore their increasing importance, I occasionally work on benchmarks for LLMs.
Please do not contact me with unsolicited offers for this kind of work.

I am supported by NSF GRFP no. 2023356980.
I am also grateful for the support of the Berkeley Connect Research Fellowship and the UC Chancellor's Fellowship.

Research and Other Writing

Undergrad Research

On the Berkovich Projective Line and Coarse-Grainings of Non-Archimedean Product Spaces (e-print 2023).

LLM Benchmarks

TBA (2026).
CAIS HLE: A benchmark of expert-level academic questions to assess AI capabilities (Nature 2026).

Misc

Some notes on Lie theory.
Milnor Excision and Beauville-Laszlo Formal Gluing.
Approximating the All-Pairs Geodesic Matrix.

Seminars Organized

Quantum Groups and Affine Lie Algebras, Spring 2026
Supersymmetry and Supergeometry, Fall 2024
Geometric Representation Theory, Spring 2024

Teaching

Graduate Student Instructor - UC Berkeley

Spring 2025: Math 98BC and Math 198BC, Berkeley Connect (instructor of record)
Fall 2024: Math 98BC and Math 198BC, Berkeley Connect (instructor of record)
Summer 2024: Math 54, Linear Algebra & Differential Equations with Arun Sharma

Teaching Assistant - USC

Fall 2022: Math 118, Fundamentals of Calculus with Danjoseph Quijada
Spring 2022: Math 226, Multivariable Calculus with Zhaoyu Zhang

People who have influenced me mathematically

(Non-exhaustive, sorted alphabetically, subject to change)
Francis Bonahon
Robert Guralnick
Cris Negrón
Sarthak Parikh
Vera Serganova

Trivial
Any opinions, findings, and conclusions or recommendations expressed in material on this page are my own and do not necessarily reflect the views of the National Science Foundation or the University of California.