Colloquia & Seminars

Title: Abelian duality via derived geometry

Quantum Field Theory and Physical Mathematics Seminar Speaker: Owen Gwilliam, Umass Amherst Title: Abelian duality via derived geometry Abstract: We discuss how to synthesize differential cohomology and the BV formalism to describe generalized Maxwell theories (or abelian p-form gauge theories), and how this framework allows a succinct formulation of abelian duality. Given time, we will discuss how these methods apply to the 6d self-dual 2-form gauge theory that appears as part of the 6d N=(1,0) and (2,0) superconformal theories known as abelian tensor multiplets. This is joint work in progress with Chris Elliott, Ingmar Saberi, and Brian Williams.

Title: Facets of link homology

Colloquium Speaker: Mikhail Khovanov, Johns Hopkins University Title: Facets of link homology Abstract: We will review some link homology theories of algebraic origin and their connections to representation theory and geometry.

Title: Geometry and Quantum Theory Seminar

Geometry and Quantum Theory Seminar Speakers: Max Hübner and Saman Habibi Esfahani

Title: CMSA Q&A Seminar

CMSA Q&A Seminar Details TBA

Title: Scaling Stochastic Momentum from Theory to LLMs

New Technologies in Mathematics Seminar Speaker: Courtney Paquette, McGill University Title: Scaling Stochastic Momentum from Theory to LLMs Abstract: Given the massive scale of modern ML models, we now often get only a single shot to train them effectively. This limits our ability to sweep architectures and hyperparameters, making it essential to understand how learning algorithms scale so insights from small models transfer to large ones. In this talk, I present a framework for analyzing scaling laws of stochastic momentum methods using a power-law random features model, leveraging tools from high-dimensional probability and random matrix theory. We show that standard SGD with momentum does not improve scaling exponents, while dimension-adapted Nesterov acceleration (DANA)—which explicitly adapts momentum to model size and data/target complexity—achieves...

Title: Higher Symmetries, Eta Invariants and Anomaly Theories 

Differential Geometry and Physics Seminar Speaker: Mirjam Cvetic, University of Pennsylvania Title: Higher Symmetries, Eta Invariants and Anomaly Theories Abstract: In recent years, much progress has been made in understanding the extra-dimensional origin of higher symmetry structures of many quantum field theories (QFTs) obtained via geometric engineering. Among others, our understanding of anomaly structures in QFTs has been significantly improved. Key in these considerations is the asymptotic boundary of the internal dimensions which geometrizes many topological QFT features. Within this context we present explicit results for anomaly coefficients in five-dimensional supersymmetric QFTs that are engineered in M-theory on Calabi-Yau three-folds, and show that eta-invariants of the asymptotic boundary of the engineered geometry are key to determine 1-form self-anomaly coefficients. The results...

Title: Algebra Seminar

Algebra Seminar  

Title: Member Seminar

Member Seminar Speaker: Saman Habibi Esfahani

Title: Quantum Field Theory and Physical Mathematics

Quantum Field Theory and Physical Mathematics Seminar

Title: Colloquium

Colloquium Speaker: L. Mahadevan, Harvard

Title: Solitonic Symmetry: Cohomology with TFT Coefficients

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 acts generically on topological defects determined by homotopy classes of maps to a “space of fields.” We will argue that the structure of solitonic symmetry in a theory with field space (Y) assembles into what looks like the cohomology of (Y) with coefficients in TFTs. We study this formalism in examples and show in particular that the maximal invertible solitonic subsymmetry reduces to...

Title: Differential Geometry and Physics Seminar

Differential Geometry and Physics Seminar Speaker: Vivek Shende (Syddansk Universitet & UC Berkeley)

Title: Member Seminar

Member Seminar Speaker: tba

Title: Freedman Seminar: Jeongwan Haah, Stanford and Mattie Ji, Penn

Freedman Seminar Speakers: Jeongwan Haah (Stanford) and Mattie Ji (Penn)  

Title: Member Seminar

Member Seminar Speaker: tba