I am a ~~first-~~second-year PhD student at Columbia interested in number theory and arithmetic geometry. (Also, dead languages, music, and many other things.)

Email: avizeff\(@\)math.columbia.edu.

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:

Expository writing for an audience which is approximately me:

- Statement and outline of the proof of Gross-Zagier
- The case $N = 1$: on singular moduli
- A deformation-theoretic proof of a counting lemma
- Counting supersingular curves with level structure via the Langlands-Kottwitz method, following Scholze
- Notes on Howard-Yang's singular moduli

- 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. My beloved. I know no one needs me to link Wikipedia as a resource, but I can't just not.

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.)