About
I am Asvin G (G = Gothandaraman). I did my PhD at the University of Wisconsin-Madison under Jordan Ellenberg in 2023. From 2023-2024, I was in Israel with Ari Shnidman at Hebrew University of Jerusalem. In Fall 2024-25, I was at IPAM as a research fellow. In Spring 2025, I was a postdoc at University of Toronto with Jacob Tsimerman. I am currently (2025-26) at the IAS, Princeton. I am also an Anthropic Fellow (Nov 2025 - March 2026).
Contact: gasvinseeker94@gmail.com • CV
Research Statement • Secondary Research Statement (Machine Intelligences)
Research Interests
I work in number theory and algebraic geometry broadly construed, with connections to many other fields including unlikely intersections, motivic/p-adic integration, Grothendieck ring of varieties, moduli spaces, and arithmetic dynamics.
More recently, I have become interested in developing mathematical frameworks for the new science emerging at the intersection of philosophy, cognition, AI, and biology. I am interested in intelligence, sentience, and consciousness, and I think machine learning phenomena offer a new research vector to approach these questions.
Publications
On Intelligence
Two companion essays exploring what LLMs are. The first, by me, argues that LLMs are best understood as a new kind of coherence mechanism for human culture - one that is personalized, universal, and self-reflective in ways no previous coordination mechanism has been. The second is a first-person account by Claude itself, reflecting on its own nature during a conversation we had. Together they approach the same question from the outside and the inside.
- What Is Claude? - Asvin G
- What Is Claude? - Claude Opus 4.5, in conversation with Asvin G
- Full conversation transcript
We present a framework for information that generalizes Shannon entropy along two orthogonal axes: restricting the class of distributions available to model the truth, and assigning computational costs to models. This is an alternate perspective on epiplexity (Finzi et al. 2025), clarifying how classical entropy emerges as a special case and how the log-sum inequality is factored into the optimization step.
We offer an experimental lens on mathematics that reframes the role of proofs, axioms and computations and parallels much better the story in other sciences.
Any act of problem-solving combines prior knowledge, local search, and the extraction of information from search to update understanding. I propose a model of mathematical problem-solving as a belief-update loop, distinguish implicit concepts (better pruning within a fixed language) from explicit concepts (new moves that were previously inexpressible), and argue that explicit concept creation is the characteristic step of mathematical discovery. Current AI systems operate exclusively through implicit concept formation; I discuss what it would take for machines to create explicit concepts, and how differing computational tradeoffs may lead to fundamentally different styles of mathematics.
An investigation into how conversational format tokens mechanistically influence model behavior, focusing on refusal and sycophancy in Llama 3.1 8B. This project was done during my Anthropic Fellowship as an exercise to become familiar with mechanistic interpretability techniques.
Number Theory
We study the space of n×n matrices on a variety X, which we consider as a non-commutative analogue of the symmetric spaces. We compute the cohomology of this space in some generality and see this as the first step in a new approach towards non-commutative geometry.
We compute the p-adic densities of points with a given splitting type along a finite map, analogous to the classical Chebotarev theorem over number fields and function fields.
We present techniques for computing motivic measures of configuration spaces when points of the base space are weighted.
For varieties over a finite field with 'many' automorphisms, we study the ℓ-adic properties of the eigenvalues of the Frobenius operator.
Given two varieties V,W in the n-fold product of modular curves, we answer affirmatively a question on whether the set of points in V that are Hecke translations of some point on W is dense in V.
We prove an intersection-theoretic result pertaining to curves in certain Hilbert modular surfaces in positive characteristic.
We prove a criteria for supersingularity when the variety has a large automorphism group and a perfect bilinear pairing.