# Alessio Figalli: Free boundary regularity for the obstacle problem

**Time: **
Wed 2022-11-02 15.15 - 17.00

**Location: **
KTH, K1

**Participating: **
Alessio Figalli (ETH Zurich)

#### Location

**K1**, KTH.

#### Schedule

14:15–15:00 Pre-colloquium by Sunghan Kim in E52

15:15–15:30 SMC prizes for the academic year 2021/2022 will be announced and awarded.

15:30–16:30 Colloquium lecture by Alessio Figalli.

16:30–17:00 SMC social get together with refreshments.

#### Abstract

The classical obstacle problem consists of finding the equilibrium position of an elastic membrane whose boundary is held fixed and which is constrained to lie above a given obstacle. By classical results of Caffarelli, the free boundary is smooth outside a set of singular points. However, explicit examples show that the singular set could be, in general, as large as the regular set. This talk aims to introduce this beautiful problem and describe some classical and recent results on the regularity of the free boundary.