About

I am Asvin G (sometimes written as Asvin Gothandaraman), currently a fifth year math PhD student at the University of Wisconsin-Madison. I am advised by Jordan Ellenberg. I will graduate Summer 2023 and am on the job market now.

I am interested in Number Theory, Algebraic Geometry and their connections to other fields. I have an inactive blog here and a mathoverflow page here. Here are a few notes I wrote a long time ago.

You can contact me at gasvinseeker94@gmail.com.

CV.

Research Statement.

Papers and preprints

My public author-identifier on arxiv.

[arxiv] A Chebotarev Density Theorem over Local Fields with Yifan Wei and John Yin.

We formulate and prove an analogue of the Chebotarev density theorem over local fields. We show that these densities satisfy a functional equation and as a consequence, prove a conjecture of Bhargava, Cremona, Fisher and Gajović about splitting densities of p-adic polynomials.

[arxiv] Configuration spaces, graded spaces, and polysymmetric functions with Andrew O’Desky.

We explain how to compute motivic invariants of generalized configuration space of which a motivating example is the space of irreducible multivariable polynomials in some fixed degree. To do this, we define a purely combinatorial generalization of the classical theory of symmetric polynomials by allowing variables of different weights. The key innovation is the notion of a type, generalizing partitions.

[arxiv] On the variation of the Frobenius in a non abelian Iwasawa tower.

We prove a convergence result for the characteristic polynomials of the Frobenius action on the etale cohomology in l-adic towers of curves over a finite field. The key tool is a generalization of Fermat’s little theorem to matrices.

[arxiv] Unlikely and just likely intersections for high dimensional families of elliptic curves.

We provide counterexamples to a heuristic of Shankar-Tsimerman regarding unlikely intersections in a Shimura variety. In the positive direction, we prove a conjecture formulated by Shou-Wu Zhang’s AIM group regarding just-likely intersections in a product of modular curves.

[arxiv] Just-likely intersections on Hilbert modular surfaces with Qiao He and Ananth N. Shankar.

We prove a conjecture on just-likely intersections in Shimura varieties formulated by Shou-Wu Zhang’s AIM group for Hilbert modular varieties with some mild restrictions.

Not for publication

[arxiv] Supersingularity of Motives with Complex Multiplication and a Twisted Polarization.

This short note proves a simple criterion for a variety to have supersingular cohomology when it has a large group of automorphisms and an inner product. This criterion recovers many well known results in the literature.

Miscellany

Some useful advice on writing from Poonen.

A note on Weil restrictions from the stacks workshop 2017: Weil restriction for schemes and beyond.