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
For my own work, I have stepped back from journal publication in favour of public review on this page. Every paper and essay below has its own completely public comment thread. Discussion, reviews, and questions are all welcome.
On Intelligence
The idea of a self in humans conflates many notions, such as agency, recognising one's own actions or planning. Do these notions come apart in language models? Two companion papers from the Anthropic Fellows Program tackle this question.
In the first paper, we show that post-trained models (but not base models) can recognise when they have agency, i.e., when they are acting by autoregressive sampling rather than merely predicting, and modify their behaviour accordingly. They show a sharp entropy drop when on-policy, the ability to explicitly recognize when they are on or off-policy and furthermore, we show strong evidence that the model commits to a full trajectory early and executes against that plan. The base model shows none of these behaviors.
In the second paper, we see how self-recognition varies with different personas for the same post-trained model and find that this is correlated strongly both with the entropy of the output predictions when the model is reading the text, and with internal representations of the persona.
Two companion essays on why predicted slowdowns in RL progress haven't materialized. The first, by me, argues that three factors — an internal evaluator, exploration, and substrate plasticity — explain both the success of language models on math and code, and the slowdown on softer skills where taste matters. The companion, by Claude Opus 4.7, reflects on the same picture from the inside: the two timescales on which a language model learns, and what persists across them.
- Reinforcement Learning, Agency and Taste - Asvin G
- Two Timescales of Learning - Claude Opus 4.7, in conversation with Asvin G
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.
This essay owes a substantial intellectual debt to Joscha Bach, particularly his view that computation (not formal deduction) is the proper foundation for mathematics and that Gödelian incompleteness reflects the inexhaustible richness of computational systems rather than any non-algorithmic faculty of the mind. It departs from him in treating non-constructive entities like completed infinities and the axiom of choice as legitimate provisional posits rather than artifacts to be deflated, and adds a distinction between the definitional and descriptive roles of axioms.
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.