The operadic structure on the moduli spaces of algebraic curves encodes in a combinatorial way how nodal curves in the boundary can be obtained by glueing smooth curves along marked...
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The developmental cycle of Myxococcus xanthus involves the coordination of many hundreds of thousands of cells aggregating to form mounds known as fruiting bodies. This aggregation process begins with the sequential formation...
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Over the last century, ecologists, statisticians, physicists, financial quants, and other scientists discovered that, in many examples, the sample variance approximates a power of the sample mean of each of...
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These are three concepts that examine how quantities vary: invariance and equivariance, from mathematics, and covariance, from statistics. How do they relate to each other? We will see how groups...
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Cohen and Lenstra gave a conjectural distribution for the class group of a random quadratic number field. Since the class group is the Galois group of the maximum abelian unramified...
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We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget, expert iteration, by which we mean...
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I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of...
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Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over more traditional methods have not...
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We introduce a class of random graph processes, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all...
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Consider a smooth family of hypersurfaces of degree d in P^{n+1}. When is every smooth projective limit of this family also a hypersurface? While it is easy to construct example...
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