Differential Geometry Working Seminar

Talk #1 (9:30 - 11:00 am): Daren Cheng, Department of Pure Mathematics, University of Waterloo

"A strong stability condition on minimal submanifolds and its implications, Part 1"

I will talk about the paper by C.-J. Tsai and M.-T. Wang (J. Reine Angew. Math., 2020) in which they introduce the class of "strongly stable" minimal submanifolds and generalize to these their earlier work on the uniqueness and dynamical stability (with respect to the mean curvature flow) of the zero section as a minimal submanifold in the total space of certain vector bundles equipped with special holonomy metrics. I will begin by describing the questions they want to address in the paper. Then, I will focus on the first of their two main theorems, which states that in an arbitrary Riemannian manifold, every strongly stable, closed minimal submanifold has a tubular neighborhood which contains no other closed minimal submanifolds of at least the same dimension. The proof boils down to showing that the squared distance to the given submanifold has a certain convexity property.

Talk #2 (11:20 am - 12:20 pm)

We will live stream the Rutgers Geometric Analysis Conference. The speaker is Scott Wilson, and the talk is about formality of compact complex manifolds. The full schedule for this conference is here:

https://www.sas.rutgers.edu/cms/finmath/geometric-analysis-conf-2022

MC 5403