In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did...
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Can machine learning be a useful tool for research mathematicians? There are many examples of mathematicians pioneering new technologies to aid our understanding of the mathematical world: using very early...
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Recent years have seen tremendous advances in our understanding of perturbative quantum field theory—fueled largely by discoveries (and eventual explanations and exploitation) of shocking simplicity in the mathematical form of...
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In this talk, I will survey the P=W conjecture, which describes certain structures of the cohomology of the moduli space of Higgs bundles on a curve in terms of the...
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Markov decision processes are a model for several artificial intelligence problems, such as games (chess, Go…) or robotics. At each timestep, an agent has to choose an action, then receives...
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Metals that do not fit Landau’s famous Fermi liquid paradigm of quasiparticles are plentiful in experiments, but constructing their theoretical description is a major challenge in modern quantum many-body physics. I...
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A celebrated theorem of Nash completed by Kuiper implies that every smooth Riemannian surface has a C¹ isometric embedding in the Euclidean 3-space E³. An analogous result, due to Burago...
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In this talk, I will introduce the smooth closing lemma for area-preserving diffeomorphisms on surfaces. The proof is based on a Weyl formula for PFH spectral invariants and a non-vanishing...
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I will present a construction of the object in the title which, applied to the classical Toda system, controls the theory of categorical representations of compact Lie groups, along with...
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A central challenge in quantum many-body physics is to estimate the properties of natural quantum states, such as the quantum ground states and Gibbs states. Quantum Hamiltonian complexity offers a...
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