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.

**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**Not for publication**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.