Mathematical Physics

Codimension-four ADE singularities in M-theory support non-Abelian gauge theories, and their geometric resolutions can encode branches of the vacuum moduli space. This relationship has been explored for G2 manifolds, where topologically distinct desingularisations admit interpretations as Coulomb…

Poisson sigma models sit at the intersection of deformation theory, geometry, and quantum field theory; specifically, the perturbative expansion of the two-dimensional Poisson sigma model with boundary is known to recover Kontsevich’s deformation quantization formula. In this talk, I introduce a…

Two-dimensional topological order has caught much attention in connection to topological phases of matter and topological quantum computation, in particular. It is known that tensor networks are useful tools to study mathematical structures appearing in these topics. We present recent understanding…

The assignment of scattering data to monopoles is a classical construction in gauge theory useful to understand the geometry of monopole moduli spaces; from the modern perspective, it is of interest because monopole scattering matrices are quasiclassical limits of R-matrices of shifted Yangians. I…

In this talk, I will survey joint work with Dmitri Pavlov on the construction and classification of extended geometric functorial field theories. After briefly reviewing some background and classical definitions, I will discuss the construction of the extended geometric bordism category and present…

Categorical spectra generalize spectra by allowing each level to be a pointed (∞,∞)-category rather than a space(=(∞,0)-category). After reviewing facts on Gray tensor products and stability of Gray-enriched categories, we will focus on what happens when we ask each level to have adjoints. We will…

Various operations on two-dimensional quantum field theories such as the GSO projection and various dualities involve a sum over spin structures. This talk will discuss a subtle mod-16 anomaly in the spin structure, extending the usual mod-8 anomaly of fermion parity, which can obstruct this sum. As…

Semisimple categorical symmetries, and their physical implications have been studied in great detail in the continuum and on the lattice. In particular, the nice properties of semisimple categories allows one to construct hamiltonians which enjoy this symmetry, and study its symmetric gapped phases…

I will say some words about nonunital categories, and tell you an awesome new theorem of McNamara and Wang: unitary QFTs are determined by their partition functions.

The amplituhedron was introduced by Arkani-Hamed and Trnka as a geometric object which "encodes" scattering amplitudes in N=4 SYM theory. One of their motivations was the Britto-Cachazo-Feng-Witten (BCFW) recursion for amplitudes, which in particular produced many different formulas for the same…

The theory of quiver varieties provides a fundamental bridge between representation theory, enumerative geometry, and physics. From 3d mirror symmetry, any quiver variety comes with a dual variety known as the Coulomb branch. A conjecture proposed by Bullimore-Dimofte-Gaiotto-Hilburn-Kim and…

Cosmological correlation functions probe the origins of structure in the universe. We view them as a prototype for time-dependent correlators and finite-temperature correlators in QFT. I will share recent work on the simple discrete geometries and spacetime pictures that control these correlators at…