Joey van der Leer Duran, University of Toronto
Richard Derryberry, University of Toronto and Perimeter Institute for Theoretical Physics
I will sketch why self-dual versions of the moduli of G-Higgs bundles are expected to arise from the study of certain supersymmetric quantum field theories, including a comparison to the physical origin of the geometric Langlands program. I will then describe an extension of the Langlands duality results of Hausel-Thaddeus (G=SL(n)) and Donagi-Pantev (arbitrary reductive G) that yields self-dual moduli spaces as a corollary.
MC 5403
Artour Tomberg, Western University
Jesse Madnick, McMaster University
Hanci Chi, McMaster University
Dmitry Zakharov, Central Michigan University
Julius Ross, University of Illinois at Chicago
I will describe a surprising duality between a case of the Dirichlet problem for the Complex Homogeneous Monge-Ampere Equation and a planar flow coming from fluid mechanics called the Hele-Shaw flow. Using this we are able to prove new things about both this PDE and renowned flow. I will present this in a way that suggests that it is a special case of something much more general, and end with a discussion as to what this may be. All of this is work with David Witt-Nystrom.
MC 5403
Andriy Haydys, University of Freiburg
Unlike for the classical Seiberg-Witten equation, the moduli space of the Seiberg-Witten equation with multiple spinors may be non-compact. The boundary in this case is modelled on the Seiberg-Witten monopoles with a singularity along a codimension two subset, which is referred to as a blow up set. The purpose of this talk is to discuss a lower bound for the 1-dimensional Hausdorff measure of the blow up set when the base manifold is of dimension three.
MC 5403
Siddharth Mathur, University of Arizona
Azumaya algebras, are (etale) twisted forms of matrix rings. These objects are of great utility because they give rise to Brauer classes. Fifty years ago, Grothendieck asked whether every cohomological Brauer class has a corresponding Azumaya algebra. This question is still open even for smooth separated threefolds over the complex numbers!
Alessandro Malusà, University of Saskatchewan