Joint Math/CMSA Geometry and Quantum Theory Seminar Speaker: Lorenzo Riva, Harvard CMSA Title: TQFTs do not detect the Milnor sphere Abstract: I will talk about the recent paper of Gripaios and Randall-Williams with that title, where they prove that a functorial TQFT (i.e. a symmetric monoidal functor from the n-dimensional bordism category into a suitably […]
Geometry and Quantum Theory Seminar Speaker: Sanjay Raman, Harvard Title: Solitonic Symmetry: Cohomology with TFT Coefficients Abstract: We review the formalism of https://arxiv.org/pdf/2307.00939, which develops the theory of solitonic symmetry in quantum field theory. The algebraic structure of solitonic symmetry is determined by the fusion of topological functionals in a given path-integral formulation of topological field theory, and […]
Geometry and Quantum Theory Seminar Speakers: Max Hübner, CMSA Title: Bi-HKT Manifolds, Sigma Models, Large N=4 and their String Constructions Abstract: We continue our review of Witten's paper "Instantons and the Large N=4 Algebra". We discuss the realization of large N=4 supersymmetry in the context of supersymmetric sigma-models, and discuss and motivate string theoretic duals […]
Geometry and Quantum Theory Seminar Speaker: Saman Habibi Esfahani (CMSA) Title: Geometric structures on gauge theoretic moduli spaces Abstract: Motivated by Witten’s study of instantons on S3 x S1, we survey some classical and recent results, programs, and conjectures on geometric structures, such as symplectic and hyperkahler, on moduli spaces of instantons and monopoles on various […]
Geometry and Quantum Theory Seminar Speakers: Dan Freed and Bowen Yang, Harvard CMSA Title: More on Kubota's spectrum of invertible states Abstract: Bowen will explain a construction aptly dubbed “Kitaev’s pump” in Kubota’s paper. Time permitting, Bowen will demonstrate its ubiquity throughout the study of topological phases, where it appears under various guises. In the second hour, […]
Geometry and Quantum Theory Seminar Speaker: Daniel Spiegel, Harvard Title: The Quasi-Adiabatic Theorem and All That Abstract: Yosuke Kubota has recently made progress on understanding Kitaev's conjecture by constructing a loop spectrum consisting of spaces of quantum spin systems, indexed by spatial dimension of the lattice (arXiv: 2503.12618). After a brief reminder on the C*-algebraic […]
Geometry and Quantum Theory Seminar Speaker: tba
Geometry and Quantum Theory Seminar Speaker: Lorenzo Riva, CMSA Title: Aganagic’s invariant is Khovanov homology Abstract: Webster computed the Khovanov homology of (the closure of) a braid in terms of the action of that braid on a certain KLRW category. Aganagic proposed that the same computation could be done in the Fukaya-Seidel category of the multiplicative Coulomb […]
Geometry and Quantum Theory Seminar Speaker: Sebastian Haney, Harvard Title: Homological mirror symmetry for Coulomb branches Abstract: I will describe a result of Aganagic, Danilenko, Li, Shende, and Zhou which constructs a embeddings of certain cylindrical KLRW categories into Fukaya-Seidel categories of multiplicative Coulomb branches. This can be thought of as a homological mirror symmetry statement relating the […]
Geometry and Quantum Theory Seminar Speaker:Vasily Krylov, CMSA Title: Coulomb branches and KLRW algebras Abstract: I will introduce Coulomb branches associated to a pair of a reductive group G and its complex representation N. We will discuss their main geometric properties and examine explicit examples. I will also highlight the connection to the moduli space of monopoles. […]
Geometry and Quantum Theory Seminar Speaker: Sunghyuk Park, CMSA Title: Khovanov homology from KLRW algebras Abstract: This is the first in a four-part series, organized together with Vasily Krylov, Sebastian Haney, and Lorenzo Riva, aimed at understanding Aganagic's categorification of quantum link invariants through Coulomb branches and homological mirror symmetry. In this first talk, I will lay […]
Geometry and Quantum Theory Seminar Speaker: Dan Freed Title: A fully local extension of Chern-Simons theory Abstract: The Reshetikhin-Turaev-Witten invariants of 3-manifolds fit into a 3-dimensional topological field theory that also attaches invariants to 2-manifolds and 1-manifolds. It has long been asked to extend to invariants of 0-manifolds as well, a question that often takes […]