Speaker: Biao Lian (Princeton) Title: Integrability and chaos of 1+1d chiral edge states Abstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the […]
Speaker: Pieter Bomans, Princeton Title: Bubble instability of mIIA on AdS_4 x S^6 Abstract: Recently, a set of non-supersymmetric AdS_4 vacua of massive type IIA string theory has been constructed. These vacua are perturbatively stable with respect to the full KK spectrum of type mIIA supergravity and furthermore, they are stable against a variety of […]
Abstract: Gopakumar-Vafa invariants are integers n_beta(g) which give a virtual count of genus g curves in the class beta on a Calabi-Yau threefold. In this talk, I will give a general overview of two of the sheaf-theoretic approaches to defining these invariants: via stable pairs a la Pandharipande-Thomas (PT) and via perverse sheaves a la Maulik-Toda […]
Abstract: We consider the moduli space of abelian varieties with two marked points and a frame of the relative de Rham cohomology with boundary at these points compatible with its mixed Hodge structure. Such a moduli space gives a natural algebro-geometric framework for higher genus quasi Jacobi forms of index zero and their differential equations […]
Speaker: Tamás Hausel (IST Austria) Title: Hitchin map as spectrum of equivariant cohomology Abstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.
Speaker: Clay Cordova (U Chicago) Title: Non-Invertible Duality Defects in 3+1 Dimensions Abstract: For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a […]
https://youtu.be/h-LEf4YnWhQ Speakers: Curtis Bright, School of Computer Science, University of Windsor and Vijay Ganesh, Dept. of Electrical and Computer Engineering, University of Waterloo Title: When Computer Algebra Meets Satisfiability: A New Approach to Combinatorial Mathematics Abstract: Solvers for the Boolean satisfiability (SAT) problem have been increasingly used to resolve problems in mathematics due to their […]
Speaker: Yifan Wang (NYU) Title: Fusion Category Symmetries in Quantum Field Theory Abstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar inverti https://www.youtube.com/watch?v=p82wzcicCk8&t=72s ble symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on […]
Abstract: Black holes solutions in General Relativity are parametrized by their mass, spin and charge. In this talk, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations […]
Title: Exploring Invertibility in Image Processing and Restoration Abstract: Today’s smartphones have enabled numerous stunning visual effects from denoising to beautification, and we can share high-quality JPEG images easily on the internet, but it is still valuable for photographers and researchers to keep the original raw camera data for further post-processing (e.g., retouching) and analysis. However, the […]
Member Seminar Speaker: Chuck Doran Title: The Greene-Plesser Construction Revisited Abstract: The first known construction of mirror pairs of Calabi-Yau manifolds was the Greene-Plesser “quotient and resolve” procedure which applies to pencils of hypersurfaces in projective space. We’ll review this approach, uncover the hints it gives for some more general mirror constructions, and describe a brand-new variant […]
Abstract: Localization by cosection, first introduced by Kiem-Li in 2010, is one of the fundamental techniques used to study invariants in complex enumerative geometry. Donaldson-Thomas (DT) invariants counting sheaves on Calabi-Yau fourfolds were first defined by Borisov-Joyce in 2015 by combining derived algebraic and differential geometry. In this talk, we develop the theory of cosection localization […]