Invitation to the Joint SISSA-ICTP Webinar Colloquium by Prof. Alessio Figalli on "Generic Regularity in Obstacle Problems" on Thursday 2 July at 16:00 hrs

[ICTP Director]

Dear All,

You are most cordially invited to the Joint SISSA-ICTP Webinar 
Colloquium by Prof. Alessio Figalli on "Generic Regularity in Obstacle 
Problems",  on Thursday 2 July at 16:00 hrs.

*Pre-registration* is required at the following url: 
https://sissa-it.zoom.us/webinar/register/WN_ca93G01TQ6eO0zn99mkp-g

After registering, you will receive a confirmation email containing 
information about joining the webinar.

*Biosketch: *Alessio Figalli is Director of the Forschungsinstitut für 
Mathematik (FIM), a research institute that was founded in 1964 by Beno 
Eckmann with the objective to promote and facilitate the exchange and 
cooperation between ETH Zürich and the international mathematical 
community. He is chaired Professor at ETH Zürich (Switzerland). He works 
in the broad areas of Calculus of Variations and Partial Differential 
Equations, with particular emphasis on optimal transportation, 
Monge-Ampère equations, functional and geometric inequalities, elliptic 
PDEs of local and non-local type, free boundary problems, 
Hamilton-Jacobi equations, transport equations with rough vector-fields, 
and random matrix theory.

*In 2018, he won the Fields Medal **"for his contributions to the theory 
of optimal transport, and its application to partial differential 
equations, metric geometry, and probability".
*

*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 $C^\infty$ outside a set of 
singular points. Explicit examples show that the singular set could be 
in general $(n-1)$-dimensional that is, as large as the regular set. In 
a recent paper with Ros-Oton and Serra we show that, generically, the 
singular set has zero $\mathcal{H}^{n-4}$ measure (in particular, it has 
codimension 3 inside the free boundary), solving a conjecture of 
Schaeffer in dimension $n \leq 4$. The aim of this talk is to give an 
overview of these results.

The talk will be followed by a question/answer session.

For info, please check the following link: 
http://indico.ictp.it/event/9410/

We look forward to seeing you online!

With best regards,

Office of the Director, ICTP