Agastya Goel

I replicated human survey results by replacing human survey participants with large language models (LLMs) answering on behalf of generated personas, in order to better understand both human and LLM behavior. I introduced a key innovation: an extra modeling step after receiving LLM responses. This approach yields significantly improved predictions compared to a uniform guess, and confirms previously discovered biases in LLMs. Paper in progress..

RS-complete Cycle Types, 2022 PUBLICATION: The Australasian Journal of Combinatorics - Published PAPER: [2301.07216] RSK-Complete Cycle Decompositions https://arxiv.org/abs/2301.07216 Understanding the specific cycle decompositions achieving RSK-completeness is foundational in various mathematical areas, facilitating algorithmic improvements, combinatorial enumeration, theoretical advancements, and providing connections to representation theory and beyond. In this paper, we characterize the class of cycle decompositions that can achieve all Young tableau shapes (except the trivial ones with a single row or single column) under the Robinson–Schensted–Knuth (RSK) correspondence, a property that we call RSK-completeness. We prove that for even n, cyclic permutations comprise the only fixed cycle decomposition that is RSK-complete. For odd n, cyclic permutations and almost cyclic permutations which have a cycle of length n−1 are the only RSK-complete cycle decompositions. Invited talk at CombinaTexas 2024, Texas A&M

Arithmetic of Semisubtractive Semidomains, 2023 (Group Project, PRIMES-USA) PUBLICATION: Journal of Algebra and its Applications - Published PAPER: [2311.07060] Arithmetic of semisubtractive semidomains https://arxiv.org/abs/2311.07060 Factorization theory studies the decomposition of elements into irreducible factors within various algebraic structures. This investigation allows us to prove general results about algebraic objects based on just a few properties. A primary objective in this field is to gauge the extent to which an object deviates from having unique factorizations, and this paper almost completely answers this question with regard to semisubtractive semidomains. In this paper, we study the arithmetic of semisubtractive semidomains (i.e., semidomains S for which either s ∈ S or − s ∈ S for every s ∈ 𝒢(S)). Specifically, we provide necessary and sufficient conditions for a semisubtractive semidomain to be atomic, to satisfy the ascending chain condition on principals ideals, to be a bounded factorization semidomain, and to be a finite factorization semidomain, which subsequent relaxations of the property of having unique factorizations. This gives a near-complete characterization of the ascension and descension of these properties between integral domains and semisubtractive semidomains.