Given a moduli space of either sheaves on a smooth projective variety or a moduli space of representations of a quiver, there are several invariants that we can extract. One...
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A chaotic quantum system can be studied using the out-of-time-order correlator (OTOC). I will tell you about pole skipping — a recently discovered feature of the retarded Green’s function —...
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I will begin the talk with an overview of the topic of quantitative homogenization for elliptic and parabolic equations. Homogenization refers to the procedure of replacing a very "noisy" equation--...
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The flag variety of rank r=(r_1,...,r_k) has points corresponding to collections of subspaces (V_1,..., V_k) with V_i of dimension r_i such that V_i is contained in V_{i+1}. It can be...
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Emergent symmetry can be generalized symmetry beyond (higher) group description and/or can be anomalous. I will describe a unified theory for generalized symmetry based on symmetry/topological-order correspondence. I will also...
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Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and they give...
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In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions,...
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We prove a conjecture by Cameron and Aydinian in three dimensions, showing that the density of the largest sum-free subset of [n]^3 approaches (10 + √15)/20 as n approaches infinity....
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I discuss the impact of the positive cosmological constant on the interplay between the equivalence principle in general relativity, and the rules of quantum mechanics. There is an ambiguity in...
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***** On August 31–Sep 1, 2023 the CMSA will host the ninth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as well as scholars from across...
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