We give the first examples of codimension-1 knotting in the 4-sphere, i.e. there is a 3-ball B_1 with boundary the standard linear 2-sphere, which is not isotopic rel boundary to...
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In this talk, we will discuss a quasi-local Penrose inequality with charges for time-symmetric initial data of the Einstein-Maxwell equation. Namely, we derive a lower bound for Brown-York type quasi-local...
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The groups of homeomorphisms or diffeomorphisms of a manifold have many striking parallels with finite dimensional Lie groups. In this talk, I'll describe some of these, and explain new work,...
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I plan to sketch Kontsevich's proof of formality of the little n-disk operad, and time permitting, intrinsic formality.
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Inspired by recent constructions of Jordan-Wigner transformations in higher dimensions by Kapustin et. al., I will present a framework for an exact bosonization, which locally maps a translation-invariant model of...
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Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra....
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One of the fundamental challenges in number theory is to understand the intricate way in which the additive and multiplicative structures in the integers intertwine. We will explore a dynamical...
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I will describe how certain recursive distributional equations can be solved by importing rigorous results on the convergence of approximation schemes for degenerate PDEs, from numerical analysis. This project is...
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Let $M$ be a complete Ricci-flat manifold with Euclidean volume growth. A theorem of Colding-Minicozzi states that if a tangent cone at infinity of $M$ is smooth, then it is...
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In this work, we propose a systematical framework to construct Bell inequalities from stabilizers which are maximally violated by general stabilizer states. We show that the constructed Bell inequalities can...
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