The early 20th century witnessed an explosion of activity, much of it centered at Harvard, on rigorizing the property of ergodicity first proposed by Boltzmann in his 1898 Ergodic Hypothesis...
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Deep learning has had transformative impacts in many fields including computer vision, computational biology, and dynamics by allowing us to learn functions directly from data. However, there remain many domains...
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In recent years fruitful connections between math and physics have emerged from the study of scattering amplitudes. I will review and put into context some key concepts from this exchange...
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Please note special time I spent a portion of 2023 working with a team at DeepMind on the “cap set problem” – how large can a subset of (Z/3Z)^n be...
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The talk consists of two independent parts. In the first part, I will talk about a new model to explain the Standard Model flavor hierarchy. Our model is based on...
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It is well-understood that Gromov-Witten (GW) invariants often fail to be enumerative. For example, when r is at least 3, the higher-genus GW invariants of P^r fail to count smooth...
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We prove that along with the Einstein flow, any small perturbations of an $n$($n\geq4$)-dimensional, non-compact negative Einstein space with some "non-positive Weyl tensor” lead to a unique and global solution,...
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Stochastic partial differential equations (PDEs) find extensive applications across diverse domains such as physics, finance, biology, and engineering, serving as effective tools for modeling systems influenced by random factors. The...
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At the heart of the theory of NP completeness lies a mapping from classical circuits to constraint satisfaction problems (classical local Hamiltonians). The quantum analogue of this is the remarkable...
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This semester we will go through the work of Burklund, Hahn, Levy and Schlank on the construction of counterexamples to the telescope conjecture.
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