The study of static Riemannian metrics arises naturally in general relativity and differential geometry. A static metric produces a special Einstein manifold, and it interconnects with scalar curvature deformation and...
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The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation,...
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Current Developments in Mathematics 2021-22 March 18-19, 2022 Harvard University Science Center Lecture Hall B Speakers: Jessica Fintzen (University of Cambridge and Duke University) Ryan O’Donnell (Carnegie Mellon) Jack...
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The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program, formal and phenomenological implications, and...
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Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision and natural language processing. Along with its empirical success, deep learning has been theoretically shown to be...
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Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision and natural language processing. Along with its empirical success, deep learning has been theoretically shown to be...
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Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these...
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Billiards on an elliptical billiard table are completely integrable: phase space is foliated by invariant submanifolds for the billiard flow. Birkhoff conjectured that ellipses are the only plane domains with...
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It is by now well-known that mirror symmetry may be expressed as an equivalence between categories associated to dual Kahler manifolds. Following a proposal of Teleman, we inaugurate a program...
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I will first review the construction of the moduli space of tropical curves (or metric graphs), and its relation to graph complexes. The graph Laplacian may be interpreted as a...
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