Avi Zeff

I am a fourth-year PhD student at Columbia interested in number theory and arithmetic geometry, especially p-adic geometry and intersections on spaces of shtukas of various kinds. Many of my interests revolve around connections between number theory and various other fields, such as homotopy theory in relation to p-adic geometry, arithmetic applications of derived algebraic geometry, and the mysterious connections to physics appearing in the relative Langlands program. (Also, dead languages, music, and many other things.) My advisor is Chao Li.

Email: avizeff@math.columbia.edu.


Spring 2024 I am a TA for Undergraduate Seminars II with Alisa Knizel, running a section on additive number theory.

Fall 2023 I taught Calculus 1 (section 10); you can find some of the materials here.

Spring 2023 I was a TA for Calculus 4 with Daniela De Silva.

Fall 2022 I taught Calculus 1 (section 10); you can find some of the materials here. (Note that some aspects of the course, both in form and content, vary from the Fall 2023 version.)

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.


Fall 2022 I organized 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.

Other than talks for the seminars linked above, I've given a number of talks in other learning seminars, notes for some of which can be found here.


Note: all of these are based on my limited understanding, and many are years old; all may (and some 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:

Notes I took for my own benefit, which may also be useful as expository, likely for a grad student audience:

Other writing:

Other resources

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.)