Geometry and Quantum Theory Seminar Speaker: Sunghyuk Park, Harvard CMSA Title: Skein traces and curve counting Abstract: Skein modules are vector space-valued invariants of 3-manifolds describing the space of line defects modulo skein relations (determined by a choice of a ribbon category). When the 3-manifold is S x I for some surface S, the skein […]
Geometry and Quantum Theory Seminar Speaker: Mayuko Yamashita, Kyoto University Title: Topological Modular Forms, its equivariant refinements and relation with supersymmetric quantum field theories Abstract: This talk is about the Segal-Stolz-Teichner program, which is one of the most deep and interesting topics relating homotopy theory and physics. Mathematically, they propose a geometric model of TMF, […]
Colloquium Speaker: Artem Chernikov, University of Maryland Title: Higher Vapnik–Chervonenkis theory Abstract: Finite VC-dimension, a combinatorial property of families of sets, was discovered simultaneously by Vapnik and Chervonenkis in probabilistic learning theory, and by Shelah in model theory (where it is called NIP). It plays an important role in several areas including machine learning, combinatorics, mathematical […]
Geometry and Quantum Theory Seminar Speaker: Thibault Décoppet, Harvard University Title: Fusion 2-Categories and their Classification Abstract: Categorifying the classical notion of fusion (1-)category, fusion 2-categories were recently introduced. These objects have found many applications in Physics, most notably to the classification of topological orders, but also to the description of non-invertible symmetries in 2+1 dimensions. […]
Geometry and Quantum Theory Seminar Speaker: Ben Gammage, Harvard University Title: Boundaries and duality for 3d gauge theories Abstract: 3d N=4 supersymmetric gauge theory has a pair of topological twists, the A-model and B-model, the latter of which is also known as Rozansky-Witten theory. Conjecturally, boundary conditions for these TFTs ought to admit descriptions in […]
Colloquium Speaker: Martin Nowak (Harvard) Title: The mathematics of evolution Abstract: All living systems are guided by evolutionary dynamics. Evolution is a search process which occurs in populations of reproducing individuals. The three fundamental forces of evolution are mutation, selection and cooperation. I will present basic ideas in the mathematical description of evolutionary dynamics, including quasi-species theory, evolutionary […]
Geometry and Quantum Theory Seminar Speaker: Dan Freed, Harvard University Title: Introduction to Factorization algebras
Geometry and Quantum Theory Seminar Speakers: Mayuko Yamashita, Kyoto University Title: Factorization algebras in TQFT Abstract: This is the first in the series of our working seminars on factorization algebras/homologies. This talk focuses on locally constant factorization algebras, which correspond to Topological QFTs. I first explain they are equivalent to algebras over E_n operads and […]
Geometry and Quantum Theory Seminar Speaker: Ahsan Khan Title: Perturbative Factorization Algebras Abstract: In physics the starting point in studying a QFT is to write down an appropriate action functional. My talk will aim to sketch how this connects with the framework of factorization algebras.
Colloquium Speaker: Anastasia Volovich, Brown University Title: Mathematical Structures of Scattering Amplitudes Abstract: Planar N=4 Yang-Mills scattering amplitudes have been computed to very high loop order. They have many remarkable properties that have sparked interest from mathematicians working on combinatorics, algebraic geometry, and number theory. At the same time, several methods that have been developed […]
Colloquium Speaker: Russell Miller, CUNY Title: Computability on $\mathbb R$ and other continuum-size structures Abstract: We begin by recalling the notion of a computable function on the real numbers $\mathbb R$, developed independently by Gregorczyk and Lacombe over sixty years ago. Using this notion, we note that the real numbers that are themselves computable form […]
Geometry and Quantum Theory Seminar Speakers: Sunghyuk Park and Vasily Krylov, Harvard CMSA Title: Factorization Homology
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