In string theory one finds that states become massless as one approaches boundaries in Calabi-Yau moduli spaces. In this talk we look in the opposite direction, that is, we search...
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Quasi-normal modes are complex exponential frequencies appearing in long time expansions of solutions to linear wave equations on black hole backgrounds. They appear in particular during the ringdown phase of...
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McMullen proved that a stable family of rational maps is either trivial or all its members are Lattès. His proof relies on Thurston's theorem on postcritically finite maps, which uses...
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My lab is developing biophysical methods to achieve multicolor and dynamic biological imaging at the molecular scale. Our approach to capturing the dynamics of cellular processes involves cryo-vitrifying samples after...
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I will discuss joint work with Christin Bibby, Nir Gadish, and Claudia Yun. The historical antecedents are in earlier work of Billera-Holmes-Vogtmann around 2000 and others, who study an interesting space of metric...
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This seminar will be held in Science Center 530 at 4:00pm on Wednesday, November 16th. Please see the seminar page for more details: https://www.math.harvard.edu/~ctm/sem
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In this talk, we describe the first polynomial time algorithm for robustly clustering a mixture of statistically-separated, high-dimensional Gaussians. Prior to our work this question was open even in the...
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To a connected reductive group G over a local field F we define a compact topological group π_1~(G) and an extension G(F)_∞ of G(F) by π_1~(G). From any character x of π_1~(G) of order...
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In nature, symmetry governs regularities, while symmetry breaking brings texture. In artificial neural networks, symmetry has been a central design principle, but the role of symmetry breaking is not well...
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When a collection of electronic excitations are strongly coupled to a single mode cavity, mixed light-matter excitations called polaritons are created. The situation is especially interesting when the strength of...
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