Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields: Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity. The remarkable richness of […]
Abstract: I will report on a project which aims to encode the DT invariants of a CY3 triangulated category in a geometric structure on its stability space. I will focus on a class of categories whose stability spaces were studied in previous joint work with Ivan Smith, and which correspond in physics to theories of class […]
https://youtu.be/USKZjJ8_LI0 Speaker: Achilleas Porfyriadis, Harvard Black Hole Initiative Title: Extreme Black Holes: Anabasis and Accidental Symmetry Abstract: The near-horizon region of black holes near extremality is universally AdS_2-like. In this talk I will concentrate on the simplest example of AdS_2 x S^2 as the near-horizon of (near-)extreme Reissner-Nordstrom. I will first explain the SL(2)transformation properties of the spherically […]
Abstract: The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterized by swirls, jets, and topological disclinations in their orientation field. I will first discuss two examples of these collective features helping us understand biological processes: (i) to explain the tortoise & hare story in bacterial competition: […]
Abstract: In this talk we describe a new method to study the singular set in the obstacle problem. This method does not depend on monotonicity formulae and works for fully nonlinear elliptic operators. The result we get matches the best-known result for the case of Laplacian.
Abstract: Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, […]
Abstract: Eugene Wachspress introduced polypols as real bounded semialgebraic sets in the plane that generalize polygons. He aimed to generalize barycentric coordinates from triangles to arbitrary polygons and further to polypols. For this, he defined the adjoint curve of a rational polypol. In the study of scattering amplitudes in physics, positive geometries are real semialgebraic […]
Abstract: This is a report about work in progress with: Adeel Khan, Aloysha Latyntsev, Hyeonjun Park and Charanya Ravi. We will describe a virtual Atiyah-Bott formula for Artin stacks. In the Deligne-Mumford case our methods allow us to remove the global resolution hypothesis for the virtual normal bundle.
Minicourses General Relativity Program Minicourses During the Spring 2022 semester, the CMSA hosted a program on General Relativity. This semester-long program included four minicourses running in March, April, and May; a conference April 4–8, 2022; and a workshop from May 2–5, 2022. Schedule Speaker Title Abstract March 1 – 3, 2022 10:00 am – […]
Speaker: Richard Kenyon (Yale) Title: Dimers and webs Abstract: 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 independent dimer covers (or “n-webs”). This is joint work with Dan Douglas and Haolin Shi.
Abstract: The SYZ proposal suggests that mirror symmetry is T-duality. It is a folklore that locally free sheaves are mirror to a Lagrangian multi-section of the SYZ fibration. In this talk, I will introduce the notion of tropical Lagrangian multi-sections and discuss how to obtain from such object to a class of locally free sheaves on the log Calabi-Yau spaces that Gross-Siebert have considered. I will also discuss a joint work […]