Kenz Kallal
Princeton University Department of Mathematics
Fine Hall, Washington Road
Princeton, NJ 08544
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kallal[at]princeton[dot]edu |
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I am a third year Ph.D. student in Mathematics at Princeton University. I passed my general examination in April 2023, and I am very fortunate to be advised by Akshay Venkatesh.
I graduated from Harvard in 2021 with an A.B. in Mathematics and an S.M. in Computer Science. I graduated from Université Paris-Sud, Orsay (Paris XI, now considered part of Université Paris-Saclay) with an M2 master's degree in 2022.
My graduate studies have been generously supported by the Commission Fulbright Franco-Américaine, the Fondation Mathématique Jacques Hadamard, and the United States National Science Foundation Graduate Research Fellowship Program.
I was very fortunate to have been advised by Mark Kisin for my undergraduate thesis, and by Gaëtan Chenevier for my master's thesis ("mémoire de M2"). I was also mentored by Ahmed Abbes as a visitor to I.H.E.S. during 2021-2022.
Here are my undergraduate thesis, M2 mémoire, and CV.
Research interests:
(p-adic) automorphic forms and Galois representations, eigenvarieties, Langlands program, arithmetic statistics.
Publications:
2. Kenz Kallal and Hudson Kirkpatrick. Ramification of wild automorphisms of Laurent series fields. [arXiv:1611.01077]
Proceedings of the American Mathematical Society, 149:991-1009 (2021).
1. Kenz Kallal, Tomoka Kan, and Eric Wang. Improved lower bounds for kissing numbers in dimensions 25 through 31. [arXiv:1608.07270]
SIAM Journal on Discrete Mathematics, 31(3):1895-1908 (2017).
Expository articles and notes:
- Theta functions and the metaplectic group, summer 2023. [Notes for a PROMYS guest lecture I gave at Boston University]
- Artin L-functions, fall 2022. [Notes I wrote up for two talks I gave in the Skinner-Venkatesh learning seminar on the Stark conjectures at Princeton/IAS]
- Automorphic forms and the Selberg trace formula, summer 2020. [Written up for the University of Chicago graduate students' automorphic seminar; NB: most but not all of this is contained in my undergraduate thesis]
- A new(?) proof of the Gauss--Siegel asymptotic averaging formula for class numbers of real quadratic fields, spring 2020. [My final project for Fabian Gundlach's graduate arithmetic statistics topics course]
- Finite flat group schemes, spring 2020. [Notes from a reading course mentored by Barry Mazur on group schemes and abelian varieties; joint with Matthew Hase-Liu]
- Class field theory, summer 2019. [Mentored by Mark Kisin]
Course notes:
As an undergraduate at Harvard, I was the course assistant for two courses on algebraic number theory: an undergraduate course taught by Mark Kisin, and a graduate course taught by Fabian Gundlach. I took notes for both of these courses, which some people have found useful:
- Math 223a: Algebraic Number Theory, fall 2019.
- Math 129: Number Fields, spring 2019.
Miscellaneous:
- Errata for Bump's book on automorphic forms and representations [some contributions from me and Robin Zhang, though it was mostly written by Sam Mundy and Pak-Hin Lee]
- My work on measuring gerrymandering with persistent homology, 2019