We apply the formalism of quantum field theory and Euclidean space-time path integral to investigate a class of quantum information problems. In particular, we investigate quantum many-body systems under weak-measurement...
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Random surfaces are central paradigms in equilibrium statistical mechanics. As these surfaces become larger, their statistical behaviors become strongly dependent on how their boundaries are pinned down. This can lead...
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The more prosaic cousin of active matter, driven inactive matter, is still full of unexpected phenomena. I will discuss two projects involving two seemingly mundane systems, a phase-separating colloidal mixture...
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A parking function is a sequence (a_1,…,a_n) of positive integers such that if b_1<=…<=b_n is the increasing rearrangement of a_1,…,a_n, then b_i<=i for 1<=i<=n. Parking functions of length n are...
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A dimer tiling of Z^d is a collection of edges such that every vertex is covered exactly once. In 2000, Cohn, Kenyon, and Propp showed that 2D dimer tilings satisfy...
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We prove, for any prime ∫ greater than or equal to 5, that a density one set of rational elliptic curves are ∫-Diophantine stable in the sense of Mazur and...
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Transformers can be trained to solve problems of mathematics. I present two recent applications, in mathematics and physics: predicting integer sequences, and discovering the properties of scattering amplitudes in a...
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Crepant resolutions have inspired connections between birational geometry, derived categories, representation theory, and motivic integration. In this talk, we prove that every variety with log-terminal singularities admits a crepant resolution...
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The amplitude/Wilson loop correspondence identifies planar N=4 super-Yang-Mills amplitudes with certain null polygonal Wilson loops at all the values of the coupling. At strong coupling this equates the amplitude/Wilson loop...
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One of the strangest consequences of the Axiom of Choice is the following Hardin-Taylor 2008 result: there is a "predictor" such that for every function $f$ from the reals to...
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