Differential Geometry Working Seminar

Talk #1 (9:30-10:45): Tommaso Pacini, University of Torino, live via Zoom

Title: One theorem, three points of view
Abstract: Consider the standard 2-sphere. Rotations around the z-axis generate a family of orbits, containing a unique maximal orbit: the equator (a geodesic). The 2-sphere is Kahler, and rotations are isometries. It turns out that the above picture generalizes to this broad context (which includes for example toric manifolds), leading to an interesting interplay between (i) curvature and volume, (ii) potential theory and Riemannian submersions, (iii) Riemannian, complex and symplectic geometry. We will also discuss extensions to the recent potential theory on calibrated manifolds due to Harvey-Lawson.

Talk #2 (11:00-12:15): Amanda Petcu, Department of Pure Mathematics, University of Waterloo

Title: An Introduction to Kahler Geometry: Part 1
Abstract: This talk will focus on the background knowledge needed to begin studying Kahler Geometry. In particular we will focus on building knowledge of complex geometry. We will introduce complex manifolds and almost complex manifolds, as well as holomorphic forms and vector fields and, holomorphic vector bundles. We will examine a few examples and theorems of integrable structures and holomorphic structures. Lastly, we might even talk about Kahler metrics if I get to it in time.

MC 5403