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

ICTP/director director at ictp.it
Thu Jul 2 12:26:10 CEST 2020

Dear All,

You are most cordially invited to the Joint SISSA-ICTP Webinar
Colloquium by Prof. Alessio Figalli on "Generic Regularity in Obstacle
Problems",  TODAY, 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.

The Colloquium will be screened in Budinich Lecture Hall (max 10 persons
can attend on a first-come, first-served basis). Please follow the
precautionary measures by respecting the distance between persons and
wearing your mask.

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

This is an event towards ESOF2020. https://www.esof.eu/en/home.html

We look forward to seeing you online!

With best regards,

Office of the Director, ICTP



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