Rahul Dalal

I currently work at Succinct building zero-knowledge/succinct proof systems and hopefully exploring if there are useful connections to some of my pure-math work through constructions of expander complexes.

Previously I was a postdoc with Alberto Minguez at the University of Vienna and an NSF postdoc at Johns Hopkins sponsored by Yiannis Sakellaridis. My academic math interests are in automorphic representations and the trace formula.

My Ph.D. was from UC Berkeley advised by Sug Woo Shin. Before that, I was an undergraduate at Harvard University.

Contact

Email: (firstname).(lastname)@univie.ac.at

Papers and Preprints

Constructions and Applications

(w/Tamir Hemo, Eugene Rabinovich, and Ron Rothblum) VEIL: Lightweight Zero-Knowledge for Hash-Based Multilinear Proof Systems (preprint)
We experimented with AI-assisted formal verification for this paper. The results can be found here.
Here's a proof-of-concept implementation.
(w/Alberto Mínguez and Jiandi Zou) Ramanujan Complexes from Unitary Groups over Number Fields (submitted)
(w/Shai Evra and Ori Parzanchevski) Multi-Qubit Golden Gates (preprint) Slides

Asymptotics and Equidistribution

(w/Mathilde Gerbelli-Gauthier and Simon Marshall) Uniform Bounds and Uncertainty for Asymptotics of Representations of p-adic GL_N (preprint)
(w/Mathilde Gerbelli-Gauthier) Root Number Equidistribution for Self-Dual Automorphic Representations on GL_N (submitted) Slides
(w/Mathilde Gerbelli-Gauthier) Statistics of Cohomological Automorphic Representations on Unitary Groups via the Endoscopic Classification (submitted) Slides
Here's a research-level talk on this work.
Counting Discrete, Level-1, Quaternionic Automorphic Representations on G₂ (Journal of the Institute of Mathematics of Jussieu. Published online 2023:1-31) Slides
Here's a short, research-level talk on this work.
Sato-Tate Equidistribution for Families of Automorphic Representations through the Stable Trace Formula (Algebra & Number Theory 16 (2022), no. 1, 59-137) Slides
Here's a short talk on this work for a general number theory audience.

Finally, here are some pop-science style slides on automorphic representations.

Classes Taught

At JHU:

Spring 2024: Math 212 "Honors Linear Algebra"
Fall 2023: Instructor for Math 422 "Representation Theory"
Fall 2022: Instructor for Math 304 "Elementary Number Theory"

At UC Berkeley:

Spring 2021: GSI for Math 104 "Introduction to Analysis"
Spring 2020: GSI for Math 250b "Commutative Algebra"/Math 254b "Number Theory"
Spring 2019: GSI for Math 55 "Discrete Mathematics."
Spring 2018: GSI for Math 54 "Linear Algebra and Differential Equations."
Spring 2017: GSI for Math 53 "Multivariable Calculus."
Fall 2016: GSI for Math 53 "Multivariable Calculus."
Spring 2016: GSI for Math 54 "Linear Algebra and Differential Equations."
Fall 2015: GSI for Math 1A "Calculus I."