$\ell$-torsion conjecture states that $\ell$-torsion of the class group $|\text{Cl}_K[\ell]|$ for every number field $K$ is bounded by $\text{Disc}(K)^{\epsilon}$. It follows from a classical result of Brauer-Siegel, or even earlier...
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TITLE: Immersions of manifolds and homotopy theory ABSTRACT: The interface between the study of the topology of differentiable manifolds and algebraic topology has been one of the richest areas of work...
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We discover a wide range of new nonperturbative effects in quantum gravity, namely moduli spaces of constrained instantons of the Einstein-Hilbert action. We find these instantons in all spacetime dimensions,...
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I will discuss some aspects of SYZ mirror symmetry for pairs (X,D) where X is a del Pezzo surface or a rational elliptic surface and D is an anti-canonical divisor...
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If a complex, integral, projective curve C has only planar singularities, then its Jacobian admits a natural compactification with interesting topology. Work of Oblomkov, Shende, and others suggests the existence...
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Given an n x n matrix A with bounded entries, we study the problem of testing whether A is positive semi-definite (PSD) via only a small number of queries to...
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Subfactors and K-theory are useful mechanisms for understanding modular tensor categories and conformal field theories CFT. As part of this, one issue is to try and construct or reconstruct a...
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TITLE: From Deep Learning to Deep Understanding ABSTRACT: In this talk I will discuss a couple of research directions for robust AI beyond deep neural networks. The first is the need...
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TITLE: A personal story of the 4D Poincare conjecture. ABSTRACT: The proof of PC4 involved the convergence of several historical streams. To get started: high dimensional manifold topology (Smale), a new...
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In this talk, I will discuss a reformulation of the Wilson loop in large N gauge theories in terms of matrix product states. The construction is motivated by the analysis of...
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