Events - February 2021

Christopher Lang, Department of Pure Mathematics, University of Waterloo

"The Many Faces of Monopoles"

In this talk, we introduce the four ways of looking at monopoles: solutions of the Bogomolny equations, Nahm data, spectral curves, and rational maps. We then discuss the relationships between these equivalent descriptions and some of the advantages and disadvantages of using them.

Siqi He, Simons Center, Stony Brook

"The compactness problem for the Hitchin-Simpson equations"

The Hitchin-Simpson equations defined over a Kähler manifold are first order, non-linear equations for a pair of a connection on a Hermitian vector bundle and a 1-form with values in the endomorphism bundle. We will describe the behavior of solutions to the Hitchin–Simpson equations with norms of these 1-forms unbounded. We will also discuss the deformation problem of Taubes' Z2 harmonic 1-form.

Ragini Singhal, Department of Pure Mathematics, University of Waterloo

"Six dimensional nearly Kähler manifolds of Cohomogeneity one"

We will discuss a paper by Podesta-Spiro where the authors consider six-dimensional strict nearly Kähler manifolds acted on by a compact, cohomogeneity one automorphism group G. We will see how they classify the compact manifolds of this class up to G-diffeomorphisms.

Caleb Suan, Department of Pure Mathematics, University of Waterloo

"Pinching Estimates and Eigenvalues of Curvature Operators"

In this talk, we will go through various results from the paper “Curvature Operators: Pinching Estimates and Geometric Examples” by Bourguignon and Karcher, which relate bounds on sectional curvatures of manifolds to eigenvalues of curvature operators.

Zoom meeting: https://zoom.us/j/93324862932?pwd=dUdCMGJZL1A3UTBpOXVYNVROdHpKUT09