Let C be a genus 3 curve whose Jacobian is geometrically simple and has geometric endomorphism algebra equal to an imaginary quadratic field. In particular, consider Picard curves y^3 =...
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A recent achievement in K-stability of Fano varieties is an algebro-geometric construction of a projective moduli space of K-polystable Fanos. The ample line bundle on this moduli space is the...
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The Kerr black hole stability problem is an important open problem in general relativity. In this talk, I will focus on the role of energy methods in the axisymmetric stability...
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The purpose of dimension reduction methods for data visualization is to project high dimensional data to 2 or 3 dimensions so that humans can understand some of its structure. In...
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The objects of arithmetic geometry are not manifolds. Some concepts from differential geometry admit analogues in arithmetic, but they are not straightforward. How then can we hope to make precise...
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We will discuss an algebraic method by J. Huang to bound the singularity probability of the adjacency matrix of random d-regular digraphs. Although we can slightly improve the bounds, the...
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The Vafa-Witten equations (with or without a mass term) constitute a non-linear, first order system of differential equations on a given oriented, compact, Riemannian 4-manifold. Because these are the variational...
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A common theme throughout mathematics is the search for "constructive" solutions to problems as opposed to mere existence results. For problems over R and other well-behaved spaces, this idea is...
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The last decade has produced a number of remarkable discoveries, such as the first direct observation of gravitational waves by the LIGO/Virgo collaboration and the first black hole image taken by...
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Spontaneous breaking of symmetries leads to universal phenomena. We extend this notion to (−1)-form U(1) symmetries. The spontaneous breaking is diagnosed by a dependence of the vacuum energy on constant...
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