Date/Time
Date(s) - 13/12/2024
11:30 am - 12:30 pm

Location: Hamilton Hall, Room 312

Speaker: Anna Skorobogatova (ETH-Switzerland)

Title: Mod(q) area-minimizing surfaces: singularities and structure

Abstract: One possible framework in which to study the Plateau problem is by using currents with multiplicities modulo q, for a fixed integer q. This setting allows for minimizing surfaces to exhibit codimension 1 singularities like triple junctions, and has close connections to the known regularity theory for stable minimal surfaces.

In this talk, I will discuss joint work with Camillo De Lellis and Paul Minter where we establish a structural result on the singular set when the surface has higher codimension, which is an analogue of that known for hypersurfaces. I will emphasize the difficulties that arise here in contrast to the codimension 1 setting. I will also discuss work in progress with Luca Spolaor and Salvatore Stuvard on a more precise structure for two dimensional mod(q) hypersurfaces near flat singularities.