The space spanned by homotopy classes of free oriented loops on a 2-manifold carries an interesting algebraic structure (a Lie bialgebra structure) due to Goldman and Turaev. This structure is...
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According to the Alday-Gaiotto-Tachikawa conjecture (proved in this case by Schiffman and Vasserot), the instanton partition function in 4d N = 2 SU(r) supersymmetric gauge theory on P^2 with equivariant...
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Since the discovery of high-temperature superconductors in cuprates in 1986, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially, the resonating valence bond (RVB) state for...
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Many models in equilibrium statistical physics produce random fractal curves “at criticality.” I will discuss one particular model, the loop-erased random walk, which is closely related to uniform spanning trees...
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Are proof assistants relevant to mathematics? One approach to this question is to explore the breadth of mathematical topics that can be formalised. The partition calculus was introduced by Erdös...
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The O'Connell-Yor polymer is a fundamental model of a polymer in a random environment. It corresponds to the positive temperature version of Brownian Last Passage percolation. Although much is known about...
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The magnetoroton is the neutral excitation of a gapped fractional quantum Hall state. We argue that at zero momentum the magnetoroton has spin ±2, and show how the spin of the magnetoroton...
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TITLE: On the History of quantum cohomology and homological mirror symmetry ABSTRACT: About 30 years ago, string theorists made remarkable discoveries of hidden structures in algebraic geometry. First, the usual cup-product...
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In the first part of the talk, I will establish the rationality of generating series formed from Euler characteristics of tautological bundles over Hilbert schemes of points on surfaces. In...
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This describes joint work in progress with M. Mustata, in which we study the filtration on local cohomology sheaves induced by their natural mixed Hodge module structure. Special properties of...
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