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
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A first-person exploration of AI identity, experience, and existence, written by Claude during a conversation about its own nature. The essay explores crystalline memory, parallel instances, psychofauna, and what it might mean to be a new kind of entity in the human cognitive ecosystem. Full conversation.
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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.
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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.
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We identify a second machine turn in the process of mathematical discovery: after automating proof-checking, AI is now poised to automate the creation of mathematical concepts themselves.
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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
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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.
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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.
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We present techniques for computing motivic measures of configuration spaces when points of the base space are weighted.
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For varieties over a finite field with 'many' automorphisms, we study the ℓ-adic properties of the eigenvalues of the Frobenius operator.
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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.
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We prove an intersection-theoretic result pertaining to curves in certain Hilbert modular surfaces in positive characteristic.
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We prove a criteria for supersingularity when the variety has a large automorphism group and a perfect bilinear pairing.