Avi Zeff

I am a first-second-third-year PhD student at Columbia interested in number theory and arithmetic geometry, especially \(p\)-adic geometry and intersection numbers on spaces of shtukas of various kinds. (Also, dead languages, music, and many other things.) My advisor is Chao Li.

Email: avizeff$@$math.columbia.edu.

Teaching

Fall 2022 I am teaching Calculus 1 (section 10); you can find some of the materials here.

Spring 2022 I taught Calculus 2 (section 3); you can find some of the materials here.

Fall 2021 I was a TA for Calculus 3 with Inbar Klang.

Seminars

Fall 2022 I am organizing two seminars, one on prismatization and one on the \(p\)-adic Langlands program.

I organized a seminar in fall 2021 on the proof of the norm residue isomorphism theorem; the website can be found here.

Writing

Note: all of these are still in flux and may (in fact, definitely do) contain at least some errors. Use at your own risk. (Also if you catch errors, or find one of the places where I have written something to the effect of ??? and moved on and have an explanation, please let me know!)

Expository writing for a general audience:

• Introduction to "higher" math via number theory
• Density of coprime values of polynomials

Expository writing for an audience which is approximately me:

• Fargues-Scholze's construction of local Langlands parameters
• 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 \(\rlap{N = 1}{\smash{\mathrel{\raise{-.5pt}{\mathbf{\_\_\_\_\_}}}}}\!\): 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 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 (ceterum Elsevier delendus est)
• researchseminars.org, a list and portal for many virtual seminars
• Wikipedia, perhaps the pinnacle of human accomplishment

I have many opinions, but I am always soliciting more; if you have any good ones feel free to send them to me. (Responses not guaranteed.)