It is well known that, for pointed nodal curves, considering flat and proper families of pairs (X,D) leads to a proper moduli space. Still, while the notion of stable pairs...
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Fluid dynamical processes are key to understanding the formation and evolution of stars and planets. While the astrophysical community has made exceptional progress in simulating highly compressible flows, models of...
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We make the case that over the coming decade, computer assisted reasoning will become far more widely used in the mathematical sciences. This includes interactive and automatic theorem verification, symbolic...
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Homological mirror symmetry (HMS) asserts that the Fukaya category of a symplectic manifold is derived equivalent to the category of coherent sheaves on the mirror complex manifold. Without suitable enlargement...
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The Event Horizon Telescope image of the supermassive black hole in the galaxy M87 is dominated by a bright, unresolved ring. General relativity predicts that embedded within this image lies...
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Higher symmetries can emerge at low energies in a topologically ordered state with no symmetry, when some topological excitations have very high energy scales while other topological excitations have low...
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Quantum money is a cryptographic protocol for quantum computers. A quantum money protocol consists of a quantum state which can be created (by the mint) and verified (by anybody with...
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Max Dehn made many remarkable contributions to mathematics, and his name pops up in lots of places, most often in topology, where we have "Dehn surgery", the "Dehn twist", and...
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Can you use the homotopy type of the space of knots in a simply-connected 4-manifold to distinguish smooth structures? The answer is no, using embedding calculus. I will also give...
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