math (CV)

I am a PhD student in Mathematics at Stanford University. I work under the guidance of Daniel Bump on the representation theory of p-adic groups, algebraic combinatorics, and solvable lattice models.

I am a 2018 recipient of the Stanford Graduate Fellowship (the William R. Hewlett Fellow). The program was initiated by Gerhard Casper, then President of Stanford University, and is designed to support the University's commitment to attracting the very best graduate students while reducing its dependence on federal funding for PhD training.

publications

• Combinatorics of Iwahori Whittaker Functions (arxiv). I evaluate metaplectic Iwahori Whittaker Functions in terms of combinatorial objects that I call colored Lusztig data. I show that colored Lusztig data is in bijection with supersymmetric colored solvable lattice models and other colored versions of classical combinatorial data. The colored combinatorial data is associated with generalized Mirković-Vilonen cycles in affine flag varieties.
• A convergent $1/n$-expansion for GSE and GOE, arXiv preprint (2018).
• An approach to define the resultant of two entire functions, with Alexander M. Kytmanov. Complex variables and elliptic equations 62.2 (2017): 269-286.

expository papers

• Simple Proof of Tokuyama’s Formula, a post on Thuses

teaching

I am a 2021 recipient of the Robert Osserman Teaching Award. Established in 2019 and named in honor of Robert Osserman, Professor of Mathematics at Stanford from 1955 to 1990, this award honors PhD students for outstanding contributions as a TA.

See my CV for all of my teaching experience.

• Teaching assistant, Stanford MATH 53: Differential Equations with Linear Algebra, Fourier Methods, and Modern Applications, Fall 2021.
• Instructor, the Leland Scholars Program (the LSP), Summer 2021. The research poster and a class photo.
• Mentor, the Stanford Undergraduate Research Institute in Mathematics (the SURIM), Summer 2021. The final presentation and the final project.
• Teaching assistant, Stanford MATH 52: Integral Calculus of Several Variables, Spring 2021
• Teaching assistant, Stanford MATH 20: Calculus, Winter 2021
• Instructor, Stanford Pre-Collegiate Studies: Mathematical Logic and Problem Solving, Summer 2020
• Instructor, Stanford Pre-Collegiate Summer Institutes: Cryptography, Summer 2020
• Teaching assistant, Stanford University Mathematics Camp: Abstract Algebra, Summer 2020
• Mentor, Stanford Math Directed Reading Program: Game Theory, Spring 2020
• Teaching assistant, Stanford MATH 171: Fundamental Concepts of Analysis, Spring 2020

solvable lattice models seminar

I organize a weekly seminar about solvable lattice models and their applications in the representation theory of p-adic groups, algebraic geometry, combinatorics, probability, and many other fields.

We meet on Tuesdays at 2 pm PT (Pacific Time). Videos from the seminar are available on YouTube. See the seminar website for the list of speakers, announcements, notes, video recordings, and other supplementary materials.

Thuses

I created Thuses — an online publishing platform for mathematicians.

On Thuses, you can publish and discuss ideas of interest to the mathematical community. Thuses is a perfect place to share new approaches, slick proofs, and surprising counterexamples. A place for “folklore results” that are considered known but don’t actually exist in literature. A place for everything in math that just has to be shared.

We envision Thuses as a lounge in a math department, where graduate students and faculty members discuss math in front of huge blackboards. And more often than not, interesting things come up: a take on a recent arXiv paper, a “kinda known” calculation that isn’t written down anywhere, or just a desire to share what you learn with others. That’s what happens when you’re excited about math.

Thuses is the place to share your excitement.

Read more about Thuses and help us to grow.

miscellaneous

Azat Miftakhov

I created the website to support Azat Miftakhov, a mathematician and graduate student of Moscow State University, who got arrested for six years without a clear reason. It is declared that Azat has been framed by the Russian government as a result of his anarchist views.

For recent updates, follow the website created by the Azat Miftakhov committee.

writing

• How I fell in Love with Math
• If I Die
• Popular science articles (in Russian)

random