One way that mathematics grows is by finding new questions to study beyond the standard topics of serious mathematical research. We give three examples, ranging from the recreational (how many...
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Consider the set of Galois extensions L of Q whose Galois group is the quaternion group. For large X, Klüners counted extensions with |disc(L)| <= X. We discuss asymptotics when...
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In this talk, I will make connections between Graph Neural Networks (GNNs) and non-Euclidean diffusion equations. I will show that drawing on methods from the domain of differential geometry, it...
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We will consider the following problem: if (C,x_1,...,x_n) is a fixed general pointed curve, and X is a fixed target variety with general points y_1,...,y_n, then how many maps f:C ->...
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Given a polarized variation of Hodge structures, the Hodge locus is a countable union of proper algebraic subvarieties where extra Hodge classes appear. In this talk, I will explain a...
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In this talk, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions, by computing out-of-time-order correlation functions. I will...
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Let P be a convex subset of R^2. For large d, what is the smallest degree r_d of a polynomial vanishing at all lattice points in the dilate d*P? We show...
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The core entropy of a postcritically finite quadratic polynomial is the topological entropy of its restriction to its Hubbard tree. Core entropy is also the logarithm of the largest eigenvalue...
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The core entropy of a postcritically finite quadratic polynomial is the topological entropy of its restriction to its Hubbard tree. Core entropy is also the logarithm of the largest eigenvalue...
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Fluids pervade complex systems, ranging from fish schools, to bacterial colonies and nanoparticles in drug delivery. Despite its importance, little is known about the role of fluid mechanics in such...
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