1;95;0c Mathematical Sciences - George Mason University

Mathematical Sciences

College of Science

Topology, Algebraic Geometry, and Dynamics Seminar (TADS)

 

TADS is a venue for presentation/discussion concerning topology, algebraic geometry, or dynamics (broadly understood).

Attendance is open, and those interested in giving a talk should e-mail title/abstract to any committee member (dcarched, or alukyane at gmu.edu). Talks are 50-90 minutes, and will, for the time being, take place on Zoom:

ZOOM LINK.



Speakers are given the opportunity to have their presentations recorded: YouTube.

TADS Committee: David Carchedi (chair), Anton Lukyanenko


Fall 2020: Fridays 1:30-3:00 PM

  • Friday, December 4, 2020
    Notre Dame, Pavel Mnev


  • Chern-Simons theory on cylinders and generalized Hamilton-Jacobi actions


    We study the perturbative path integral of Chern-Simons theory on a cylinder [0,1]x Sigma with a holomorphic polarization on the boundaries, in the context of Batalin-Vilkovisky quantization (or rather its variant compatible with cutting-gluing, the “BV-BFV quantization”). We find that, in the case of non-abelian 3D Chern-Simons, the fiber BV integral for the system produces the gauged WZW model on Sigma. Classically, the result corresponds to computing a “generalized Hamilton-Jacobi action” for Chern-Simons theory on a cylinder — a generating function (in an appropriate sense) for the evolution relation induced on the boundary conditions by the equations of motion. A similar setup applied to 7D abelian Chern-Simons on a cylinder [0,1] x Sigma, with Sigma a Calabi-Yau of (real) dimension 6, with a linear polarization on one side and a nonlinear (Hitchin) polarization on the other side, is related to the Kodaira-Spencer (a.k.a. BCOV) theory. In the talk, I will introduce the concept of generalized Hamilton-Jacobi functions in the example of classical mechanics with constraints described by an equivariant moment map and proceed to discuss the examples above. This is a report on a joint work with Alberto S. Cattaneo and Konstantin Wernli.

  • Friday, November 20, 2020
    Cary Malkiewich, Binghamton University


  • The higher characteristic polynomial


    Abstract: In this talk I will discuss various lifts of the characteristic polynomial to the setting of algebraic K-theory, and describe the relationship to trace methods and to topological fixed-point theory and dynamics.

  • November 13, 2020
    Theo Johnson-Freyd, Dalhousie University, Perimeter Institute


  • Holomorphic SCFTs of small index


    Abstract: I will explain how some questions in theoretical physics and algebraic topology led to a curious result about error-correcting ternary codes. No knowledge of the terms in the title or abstract will be assumed. Based on joint work with Davide Gaiotto.

    Spring 2020