Lu Wang, Yale
TBA
Speaker: Keith Glennon
Title: E11 Symmetries in M Theory
Abstract: We review the argument that E11 is a symmetry of m-theory at low energies. We will suggest the possibility of an E11 symmetry based on dimensionally reduced coset symmetries of 11D SUGRA. We will argue that a certain induced representation of the semi-direct product of the very extended algebra E8+++ = E11, with its vector representation, results in the equations of motion of the bosonic sector of m-theory at low energies, predicting additional effects beyond the supergravity approximation. We will then review recent developments illustrating K27 as the 26D closed bosonic string analogue of E11, and future questions.
Polina Baron, University of Chicago
Unique ergodicity of branched covers of flat surfaces
We will start by introducing translation surfaces — flat surfaces with cone singularities and straight-line flow. These are among the simplest examples of dynamical systems, yet they model a variety of physical processes, such as Ehrenfest wind-tree models, polygonal billiards, optical cavities, and Eaton lenses. Most translation surfaces are chaotic, or, more specifically, uniquely ergodic in almost every direction: for almost every initial point, the straight trajectory equidistributes for area, and time averages equal space averages (this idea comes from Boltzmann's ergodic hypothesis in thermodynamics). After a primer where I willrndefine everything we need, I will present a new construction on translation surfaces called branched slit-induced n-cover: on a uniquely ergodic X
, pick a slit s=[P,Q]; take n copies and switch sheets i→i+1(modn) each time the vertical flow hits s (i.e., glue the copies together). It turns out that the unique ergodicity property is robust and quantifiable under such covers despite localized branching. In other words, typical micro-defects do not derail global transport statistics. This is especially notable because conditions are mostly geometric despite the measure-theoretic core of the problem. (Joint with Elizaveta Shuvaeva.)Jae Hee Lee, Stanford University
Quantum power operations and 3D mirror symmetry
In positive characteristic, on one hand the quantum connection (from Gromov--Witten theory) carries extra central endomorphisms known as quantum Steenrod operations. On the other hand, in representation theory, the algebra of differential operators also carry a "large center" in positive characteristic given by a version of the Frobenius map. I will explain how these centers are related to each other by a duality of algebraic symplectic varieties. Time permitting, I will also discuss a q-deformation of the picture involving quantum K-theory. Joint with Shaoyun Bai.
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