Gromov-Witten invariants of holomorphic symplectic 4-folds vanish and one can consider the corresponding reduced theory. In this talk, we will explain a definition of Gopakumar-Vafa type invariants for such a reduced...
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In the last three decades, the problem of consciousness - how and why physical systems such as the brain have conscious experiences - has received increasing attention among neuroscientists, psychologists,...
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In this talk I'll gently survey various roles mathematics (often, but not always, in the form of machine learning) plays in our information ecosystem. I'll discuss the math behind YouTube's...
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Consider the Gibbs distribution of the hardcore model over all independent sets of a given graph, where the probability density of each independent set J is proportional to lambda^|J| where...
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Let C be an algebraic curve over a number field. Faltings's theorem on rational points on subvarieties of abelian varieties implies that all algebraic points on C arise in algebraic...
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Characterizing many-body entanglement is one of the most important problems in quantum physics. We present our studies on the steady state von Neumann entropy and its transition in Brownian SYK...
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Gromov-Witten invariants of holomorphic symplectic 4-folds vanish and one can consider the corresponding reduced theory. In this talk, we will explain a definition of Gopakumar-Vafa type invariants for such a reduced...
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I will report a recent approach of regularizing divergent integrals on configuration spaces of Riemann surfaces, introduced by Si Li and myself in arXiv:2008.07503, with an emphasis on genus one...
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I will start the lecture with a brief introduction to various flavors of the Langlands correspondence. I will then explain the setup of a new flavor: the analytic Langlands correspondence...
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The universal centralizer of a complex semisimple adjoint group G is the family of regular centralizers in G, parametrized by the regular conjugacy classes. It has a natural symplectic structure...
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