Speaker:  Nicolaos Kapouleas  (Brown University)

Title:  Recent and ongoing work on minimal doublings and related topics

Abstract:

I will discuss doubling constructions for minimal surfaces and other recent results and ongoing work.

In particular I will discuss recent results in the article ``Generalizing the Linearized Doubling approach , I: General theory and new minimal surfaces and self-shrinkers’’, Camb. J. Math. (to appear); arXiv:2001.04240v4’', by Kapouleas-McGrath, including a new general area estimate for doublings. I will then discuss ongoing work and work on preparation, some related to recent work of Kapouleas-Wiygul in ``The index and nullity of the Lawson surfaces xig,1 Camb. J. Math. 8 (2020), 363-405 and ``The Lawson surfaces are determined by their symmetries and topology’’, J. Reine Angew. Math. 786 (2022), 155–173, which I will briefly review if there is time.