It is well-known that for any finite group G, there exists a closed 3-manifold M with G as a quotient of pi_1(M). However, we can ask more detailed questions about the possible...
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In this talk we will discuss the interaction between magnetic monopoles and massless fermions. In the 1980's Callan and Rubakov showed that in the simplest example and that fermion-monopole interactions...
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While over-parameterization is widely believed to be crucial for the success of optimization for the neural networks, most existing theories on over-parameterization do not fully explain the reason -- they...
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We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n...
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We will explore the fascinating history of counting shapes, starting with counting dots (you can have no dots or one dot or two dots...) and then moving on to counting...
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The Newell-Littlewood numbers are defined in terms of the Littlewood-Richardson coefficients. Both arise as tensor product multiplicities for a classical Lie group. A. Klyachko connected eigenvalues of sums of Hermitian...
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Inspired by an analogy between torsion and preperiodic points, Zhang has proposed a dynamical generalization of the classical Manin-Mumford and Bogomolov conjectures. A special case of these conjectures, for `split' maps, has recently...
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Scaling laws and associated downstream trends can be used as an organizing principle when thinking about current and future ML progress. I will briefly review scaling laws for generative models...
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We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime...
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We will present some rigorous results about entropy and relative entropy in QFT, motivated in part by recent physicists' work which however depends on heuristic arguments such as introducing cut off and using...
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