UCR Geometry & Topology Seminar

During the Winter 2025 quarter, all of our meetings will be held in-person in Skye Hall 268.

Talks will run from 11a-12p PT, but feel free to show up early for socializing with the speaker.

Current organizers: Brian Collier and Po-Ning Chen

You can find some of the seminar history here.

January 10 2025:

• Po-Ning Chen

Title: Near horizon limit of wang-yau quasi-local mass

Abstract:

In this talk, we discuss the behavior of the Wang-Yau quasi-local mass on a family of surfaces approaching the apparent horizon (the near horizon limit). The vanishing of the norm of the mean curvature vector implies special properties for the Wang-Yau quasi-local energy and the optimal embedding equation. We utilize these features to prove the existence and uniqueness of the optimal embedding and investigate the minimization of the Wang-Yau quasi-local energy. In particular, we prove the continuity of the quasi-local mass in the near horizon limit.

January 24, 2025:

• Brian Collier

Title: Higher rank Teichmuller spaces, what are they, how many are there and where do they come from? (Part 2)

Abstract: These two talks will be about a somewhat recent paper joint with Bradlow, Garcia-Prada, Gothen and Oliveira, where we classify and parameterize all expected higher rank Teichmuller spaces using the theory of Higgs bundles. In this first talk I will define what I mean by a higher rank Teichmuller space and motivate their classification problem and give some examples and state the main classification theorem. In the second talk I will discuss the objects used in the classification (magical sl2-triples), Higgs bundles and the parameterizing objects.

February 7, 2025:

• Tang-Kai Lee

February 21, 2025

• Jonathan Michala

March 7, 2025

• Nicki Magill