Avi Zeff
I am an RTG postdoctoral scholar at UC Berkeley, working with Tony Feng.
I did my PhD in mathematics at Columbia (2020-2025), where my advisor was Chao Li. (I am still in the process of transitioning from Columbia to Berkeley, which is why this website is still hosted on a Columbia server.)
My research interests are in number theory and arithmetic geometry broadly, and in particular in the Langlands program (broadly construed), Kudla's program and special cycles, and p-adic geometry.
Email: avizeff
Teaching
In Fall 2025 I am teaching Introduction to Complex Analysis (Math 185). Details and materials to appear soon.
Some teaching materials (syllabi, lecture notes, homework, etc.) for classes I taught in grad school can be found here.
Research
My PhD thesis is available here. The first part is joint work with Yujie Xu, on generic modularity of theta series for reductive dual pairs over function fields; a slightly strengthened version of these results should be available shortly as a separate preprint. The second part studies a p-adic analogue in a special case, which I hope to explore further.
Seminars
Some materials from seminars I organized in grad school (on the geometrization of real local Langlands; prismatization; the p-adic Langlands program; and the norm residue isomorphism theorem) can be found here.
Expository writing, notes, and miscellany
Note: many of these are years old and have not been revisited, and all may contain errors. Use at your own risk. (If you do catch errors, please let me know!)
Expository writing:
- (Some) perspectives on class field theory, for a mixed audience—most of the first section is targeted at a general audience, the second and third sections are targeted roughly at an undergraduate level, and the fourth section (on Clausen's K-theoretic Artin map) is at a graduate level
Notes I took for my own benefit, which may also be useful as expository, likely for a grad student audience:
- Fargues-Scholze's construction of local Langlands parameters
- Notes on Scholze's Emmy Noether lectures on the geometrization of real local Langlands (note: while an okay overview, these were written before more details were released; for more detailed exposition and speculation see my seminar notes)
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Notes I wrote for a reading project with Chao Li on various conjectures and proofs related to special values of L-functions (all mistakes are my own):
- Statement and outline of the proof of Gross-Zagier
- The case N = 1: on singular moduli
- A deformation-theoretic proof of a counting lemma
- Notes on Howard-Yang's singular moduli
- Counting supersingular curves with level structure via the Langlands-Kottwitz method, following Scholze
- An illustration of the Siegel-Weil formula via some simple examples
- Some notes on Shimura varieties (global and local) and modular forms/L-functions I wrote to prepare for my qualifying exams, moved to a separate page since upon rereading them they are riddled with errors and generally messily done; use at your own risk.
Other writing:
- An article some friends and I wrote for Science for the People, also featured in Jacobin
Other resources
- An article by Denis Hirschfeldt on collective power in academia generally and mathematics specifically
- The Just Mathematics Collective and in particular their statement on mathematical collaboration with the NSA and the security state more broadly
- Library Genesis, a good source of textbooks if they cannot be found in other ways - knowledge should be free!
- Sci-Hub, similarly a good source of articles
- researchseminars.org, a list and portal for many virtual seminars
- Wikipedia, perhaps the pinnacle of human accomplishment despite its flaws
- Burritos for the Hungry Mathematician, by Ed Morehouse