Title: An introduction to mean curvature flow

Abstract: The mean curvature flow can be thought of as the gradient flow for the area functional, on the space of submanifolds. In this talk I will introduce some of the basic ideas related to the mean curvature of hypersurfaces in Euclidean space, and I will describe some of the main questions.

The speaker is also our colloquium speaker the same day at 3:30 and all are welcome to attend.

Title: Singularities of generic mean curvature flows

Abstract: Surfaces evolving by mean curvature flow in R3 can develop rather complicated singularities. However, it was conjectured by Huisken that generically only very simple singularities can form. This conjecture was recently resolved by works of Chodosh-Choi-Mantoulidis-Schulze and Bamler-Kleiner. I will discuss these results, as well as what more we can say.

Professor Szekelyhidi is given a special lecture on some of the introductory...

Speaker: Dr. John T. Betts, The Boeing Company

Speaker: Jenny Paige

Title: Changing Connectivity: A Spatial Understanding of Bistable Coral Dynamics

Abstract: Modeling coral ecosystems in a theoretical framework typically focuses on tradeoffs between coral, algae, and grazing fish populations, highlighting its bistable dynamics; however, spatial understanding of this system is often suppressed. Analysis of models with spatial features is crucial, as degraded, patchy reef systems become more common, and the size, clustering, or overall...