I will explain the basics of 2-representation theory and will explain an approach to classifying 'simple' 2-representations of the Hecke 2-category (aka Soergel bimodules) for finite Coxeter types.
A group is sofic when every finite subset can be well approximated in a finite symmetric group. The outstanding question, due to Gromov, is whether every group is sofic.
Helfgott and Juschenko argued that a celebrated group constructed by Higman is unlikely to be sofic because its soficity would imply the existence of some seemingly pathological functions. I will describe joint work with Martin Kassabov and Vivian Kuperberg in which we construct variations on Higman's group and explore their soficity.
As you might expect from a man whose family included the Surrealist artist Roland Penrose, Roger Penrose has always thought visually. That thinking is captured brilliantly in this selection of Roger’s drawings that he produced for his published works and papers.
From quasi-symmetric patterns to graphic illustrations of the paradoxical three versions of reality via twistor theory and the brain, this selection captures the stunning range of Roger’s scientific work and the visual thinking that inspires and describes it.
Mezzanine Level
Mathematical Institute
Oxford
10 December 2019- 31 March 2020
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As you might expect from a man whose family included the Surrealist artist Roland Penrose, Roger Penrose has always thought visually. That thinking is captured brilliantly in this selection of Roger’s drawings that he produced for his published works and papers.
From quasi-symmetric patterns to graphic illustrations of the paradoxical three versions of reality via twistor theory and the brain, this selection captures the stunning range of Roger’s scientific work and the visual thinking that inspires and describes it.
It is known that random matrix distributions such as those that describe the largest eignevalue of the Gaussian Orthogonal and Symplectic ensembles (GOE, GSE) admit two types of representations: one in terms of a Fredholm Pfaffian and one in terms of a Fredholm determinant. The equality of the two sets of expressions has so far been established via involved computations of linear algebraic nature. We provide a structural explanation of this duality via links (old and new) between the model of last passage percolation and the irreducible characters of classical groups, in particular the general linear, symplectic and orthogonal groups, and by studying, combinatorially, how their representations decompose when restricted to certain subgroups. Based on joint work with Elia Bisi.
This lecture is about mathematical visualization: how to make accurate, effective, and beautiful pictures, models, and experiences of mathematical concepts. What is it that makes a visualization compelling?
Henry will show examples in the medium of 3D printing, as well as his work in virtual reality and spherical video. He will also discuss his experiences in teaching a project-based class on 3D printing for mathematics students.
Henry Segerman is an Associate Professor in the Department of Mathematics at Oklahoma State University.
Please email @email to register.
Watch live:
https://www.facebook.com/OxfordMathematics/
https://livestream.com/oxuni/Segerman
The Oxford Mathematics Public Lectures are generously supported by XTX Markets.
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I will discuss the geometric interpretation of the twisted index of 3d supersymmetric gauge theories on a closed Riemann surface. In the first part of the talk, I will show that the twisted index computes the virtual Euler characteristic of the moduli space of solutions to vortex equations on the Riemann surface, which can be understood algebraically as quasi-maps to the Higgs branch. I will explain 3d N=4 mirror symmetry in this context, which implies non-trivial relations between enumerative invariants associated to these moduli spaces. Finally, I will present a wall-crossing formula for these invariants derived from the gauge theory point of view.
In the talk we will define higher K-groups, and explain some of their relations to number theory
