Triangle Seminars

Abstract:
Models of random matrices can be viewed as zero-dimensional analogs of usual field theory. Despite decades of exploration, matrix models remain at the forefront of intensive research, motivated by a rich web of connections to string theory, quantum gravity, integrability, Yang-Mills theory, combinatorics, geometry and representation theory. These lectures will present a pedagogical introduction to the subject.

​Lecture 1. Motivation and basic definitions. Hermitian matrix models: Feynman rules, ribbon graphs, large N genus expansion.
Lecture 2. Reduction to eigenvalues. Large N limit, Coulomb gas approach, saddle point equations.
Lecture 3. Continuum limit of saddle point equations. Eigenvalue density and spectral curve. Examples.
Lecture 4. Orthogonal polynomials. Relation to 2d gravity and phase transitions (sketch). Outlook: loop equations, topological recursion, integrability.

Abstract:
The amplituhedron is a semi algebraic space introduced in 2013 by Arkani-Hamed and Trnka in their endeavor to understand N=4 Super Yang Mills amplitudes. A surprising property of these amplitudes is that they satisfy mysterious connections with cluster algebras. These connections are both interesting theoretically, and play a crucial role in calculating the amplitudes. In my talk I will describe the amplituhedron, the non-negative Grassmannian on which it is built,. I will then explain one of the central relations with clusters, its proof, and a recent conjectural generalization in the language of operads. Based on joint works with Chaim Even Zohar, Tsviqa Lakrec, Matteo Parisi, Melissa Sherman Bennett and Lauren Williams.

Abstract:
In this talk I will discuss features of Quantum Field Theories in a fixed de Sitter background. I will present an exactly solvable model and show how to obtain all loops correlation functions of local operators. I will then discuss the existence of charged vacuum states in the theory and its relation to spontaneous symmetry breaking in de Sitter spacetimes. 

Abstract:
We discuss properties of the gravitational path integral for rhetorics of gravity with Lambda>0. We consider the problem in various spacetime dimensions, and for various matter fields. Time permitting, we also comment on the two-dimensional case.

Abstract:
Despite recent progress, a complete formulation of a holographic correspondence for flat spacetimes remains elusive.
Any viable formulation of flat space holography should be based on a correspondence between bulk and boundary states built upon the equivalence of unitary irreducible representations (UIRs) of the asymptotic symmetry group of flat spacetimes, the BMS group. In this talk, I will present explicit wavefunctions for the UIRs of the BMS group (the so-called BMS particles). These are functions on supermomentum space that generalize the familiar notion of Poincaré particles by incorporating additional soft degrees of freedom. I will discuss their connections to infrared physics and outline prospects for defining an S-matrix for BMS states that is free from infrared divergences. This talk is based on joint work with X. Bekaert and Y. Herfray.

Abstract:
I will discuss how the technique of supersymmetric localization can be adapted to calculate exact bosonic path integrals in a class of theories where the fermions decouple from the bosons. I will then show how this method can be used to calculate the partition function of the WZW model as a sum over classical solutions. I will discuss SU(2) in some detail, as well as two related models: SL(2) and hyperbolic 3-space, i.e. Euclidean AdS3. In all these cases, the exact partition function essentially follows from the knowledge of symmetries and of free fermions.

Abstract:
Global symmetries can be generalised to transformations generated by topological operators, including cases in which the topological operator does not have an inverse. A family of such topological operators are intimately related to dualities via the procedure of half-space gauging. In this talk I will discuss the construction of non-invertible defects based on T-duality in two dimensions, generalising the well-known case of the free compact boson to any Non-Linear Sigma Model with Wess-Zumino term which is T-dualisable. I will also present several applications of this symmetry, which include the protection of some coupling constants of the sigma model from quantum corrections as well as new Ward identities. Time permitting, I'll discuss the target space interpretation of these defects, and their fate in String Theory.

Abstract:
We extend the powerful property of Yangian invariance to a new large class of conformally invariant multi-loop Feynman integrals. This leads to new highly constraining differential equations for them, making integrability visible at the level of individual Feynman graphs. Our results apply to planar Feynman diagrams in any spacetime dimension dual to an arbitrary network of intersecting straight lines on a plane (Baxter lattice), with propagator powers determined by the geometry. The graphs we consider determine correlators in the recently proposed "loom" fishnet CFTs. The construction unifies and greatly extends the known special cases of Yangian invariance to likely the most general family of integrable scalar planar graphs. We also relate these equations in certain cases to famous GKZ (Gelfand-Kapranov-Zelevinsky) hypergeometric operators, opening the way to using new powerful solution methods.