Speakers and Abstracts
Workshop on Ultra-Quantum Matter
October 25-26, 2021
Nima Arkani-Hamed, Institute for Advanced Study
Title: "Spacetime and Quantum Mechanics; Particles and "Strings"; Polytopes, Binary Geometries and Quiver Categories"
Abstract: The past decade has seen the emergence of surprising new connections between the real-world physics of elementary particle scattering processes, and simple new mathematical structures in combinatorics, algebra and geometry. These ideas provide, in a number of examples, a different starting point for conceptualizing this basic physics, where the fundamental principles of spacetime and quantum mechanics are not taken as primary, but instead emerge from a more primitive mathematical rubric. In this talk I will illustrate these ideas in their most elementary setting, showing how the simplest particle scattering amplitudes are determined by avatars of famous polytopes known as (generalized) associahedra. I will also show how the combinatorial relationships captured by the facets of these polytopes remarkably admit a "curvy" realization in terms of "binary geometries", with the physical interpretation of generalizing particles to "strings". I will finally discuss the most basic mathematical ideas underlying and generalizing these structures, involving categories of quiver representations.
Michael Levin, University of Chicago
Title: "Lattice Edge Theories for Topological Phases of Matter"
Abstract: Edge excitations of (2+1)D topological phases are usually described using continuum field theories. But the boundaries of some (2+1)D topological phases can also be described using lattice-like edge theories that have a finite dimensional Hilbert space for a finite size boundary. I will discuss several examples of such finite dimensional edge theories. The most interesting examples are ``ungappable'': they have the property that they cannot be gapped by any local interaction.