Calendar

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 and Laplacian motion, and survey what is known today including some more recent results.  I will also discuss some of the important open problems and explain why the problem is hardest in exactly three dimensions. This talk is intended for a general mathematics audience and does not assume the audience knows the terms in the previous sentence.

Zoom: https://northeastern.zoom.us/j/95962897745?pwd=UFFPV2sxUitpWGFZbVErM1kwY284Zz09

For password email Andrew McGuinness

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 (doped) spin liquids is one of the most fruitful idea. In this talk, I would like to describe the development of RVB idea to broader class of materials, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect, spin Hall effect, topological insulator, multiferroics, various topological spin textures, e.g., skyrmions, and nonlinear optics. I will show that even though the phenomena are extensive, the basic idea is rather simple and common in all of these topics.

Zoom: https://harvard.zoom.us/j/977347126

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 parameters ε₁, ε₂ is the norm of a Whittaker vector for W(gl_r) algebra. I will explain how these Whittaker vectors can be computed (at least perturbatively in the energy scale) by topological recursion for ε₁ + ε₂ = 0, and by a non-commutation version of the topological recursion in the Nekrasov-Shatashvili regime where ε₁/ε₂ is fixed. This is a joint work to appear with Bouchard, Chidambaram and Creutzig.

Zoom: https://harvard.zoom.us/j/91780604388?pwd=d3BqazFwbDZLQng0cEREclFqWkN4UT09

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 defined in terms of intersections and self-intersections of planar curves. In the talk, we will explain a surprising link between the Gaoldman-Turaev theory and the Kashiwara-Vergne problem on properties of the Baker-Campbell-Hausdorff series. Important tools in establishing this link are the non-commutative divergence cocycle and a novel characterization of conjugacy classes in free Lie algebras in terms of cyclic words. The talk is based on joint works with N. Kawazumi, Y. Kuno and F. Naef.

Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

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 defined in terms of intersections and self-intersections of planar curves. In the talk, we will explain a surprising link between the Gaoldman-Turaev theory and the Kashiwara-Vergne problem on properties of the Baker-Campbell-Hausdorff series. Important tools in establishing this link are the non-commutative divergence cocycle and a novel characterization of conjugacy classes in free Lie algebras in terms of cyclic words. The talk is based on joint works with N. Kawazumi, Y. Kuno and F. Naef.

Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09