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Alex Waldron: Lectures

September 8, 2019
TITLE: G2-instantons on the 7-sphere

ABSTRACT: I’ll discuss a forthcoming paper studying families of G_2-instantons on S^7, focusing on those which are obtained by pulling back asd instantons on S^4 via the quaternionic Hopf fibration. In the charge-1 case this yields a smooth and complete 15-dimensional family. The situation for higher charge is more complicated, but we are able to compute all the infinitesimal deformations.

June 4 and June 6, 2018
TITLE: Recent developments in Yang-Mills flow

ABSTRACT: YM flow is the basic evolution equation for a connection on a vector bundle over a Riemannian manifold. It functions both as an important tool in classical gauge theory, and as a model problem for more highly nonlinear parabolic equations (such as Ricci flow or Bryant’s Laplacian flow). In the first of two talks, I will give an introduction to the subject and describe some historical results. In the second I will describe my own results in the four-dimensional case, and briefly discuss some forthcoming work with Goncalo Oliveira characterizing blowup in the exceptional holonomy scenario.