Global Categorical Symmetries

In this talk I will review some recent progress in the study of non-invertible symmetries in dimensions d>2. After introducing known constructions and describing how they lead to constraints on RG flows, I will discuss how non-invertible symmetries can also be used to obtain new RG flows. This…

This will be an introductory discussion of our joint work with Roman Bezrukavnikov. Given a symplectic resolution X, one may study its Gromov-Witten theory and the monodromy group of the curve-counting functions in the K\"ahler variables. There is also a large group of derived autoequivalences of X…

"Motivated by applications to soft supersymmetry breaking, we revisit the Seiberg-Witten solution for N=2 super Yang-Mills theory in four dimensions with gauge group SU(N). We present a simple exact Taylor series expansion for the periods obtained at the origin of moduli space, thereby generalizing…

I'll discuss a vertex algebra whose correlators are scattering amplitudes (and form factors) of self-dual Yang-Mills theory, for certain gauge groups and matter. The vertex algebra is a kind of vertex quantum group, and is a cousin of the affine Yangian. This is joint work with Natalie Paquette.

We identify infinitely many non-invertible generalized global symmetries in QED and QCD for the real world in the massless limit. In QED, while there is no conserved Noether current for the axial symmetry because of the ABJ anomaly, for every rational angle, we construct a conserved and gauge…

I will review the analytic component of the geometric Langlands correspondence, developed recently in my joint work with E. Frenkel and D. Kazhdan (based on previous works by other authors, including A. Braverman, R. Langlands, J. Teschner, M. Kontsevich), with a special focus on archimedian local…

" I will talk about a monoidal localization theorem for the small quantum group u_q(G), where G is a reductive algebraic group and q is a root of unity. In joint work with Julia Pevtsova, we show that the category of representations for u_q(G) admits a fully faithful tensor embedding into the…

"It is possible to construct interesting field theories by placing string theory on suitable singular geometries, and adding branes. In the fairly special cases where Lagrangians are known for the resulting theories, field theory arguments often show that these theories have generalised symmetry…

We will review the role of Quantum Field Theory (QFT) in modern physics. We will highlight how QFT uses a reductionist perspective as a powerful quantitative tool relating phenomena at different length and energy scales. We will then discuss various examples motivated by string theory and lattice…

"A unitary 1d QFT consists of a Hilbert space and a Hamiltonian. A group acting on a 1d QFT is a group acting on the Hilbert space, commuting with the Hamiltonian. Note that the *data* of an action only involves the Hilbert space. The Hamiltonian is only there to provide a constraint. Moreover, all…

"Khovanov showed in ‘99 that the Jones polynomial arises as the Euler characteristic of a homology theory. The knot categorification problem is to find a general construction of knot homology groups and to explain their meaning: what are they homologies of? Homological mirror symmetry, formulated by…