# Camillo De Lellis

(Universität Zürich)

## The Onsager's Theorem I [ Video ]

** Le vendredi 24 mars 2017, 16h00, Salle 6214 / Friday, March 24, 2017, 4pm, Room 6214 **

[ Photos ]

*Cette conférence s'adresse ŕ un large auditoire.*

*This lecture is aimed at a general mathematical audience.*

In 1949, the famous physicist Lars Onsager made a quite striking statement about solutions of the incompressible Euler equations: if they are Hölder continuous for an exponent larger than 1/3, then they preserve the kinetic energy, whereas, for exponents smaller than 1/3, there are solutions which do not preserve the energy. The first part of the statement has been rigorously proved by Constantin, E and Titi in the nineties. In a series of works, László Székelyhidi and myself have introduced ideas from differential geometry and differential inclusions to construct nonconservative solutions and started a program to attack the other portion of the conjecture. After a series of partial results, due to a few authors, Phil Isett has recently fully resolved the problem. In this talk, I will try to describe as many ideas as possible and will therefore touch upon the works of several mathematicians, including László Székelyhidi, Phil Isett, Tristan Buckmaster, Sergio Conti, Sara Daneri and myself.

** Une réception suit la conférence / A reception follows. **

## The Onsager's Theorem II [ Video ]

Le lundi 27 mars 2017, 16h00, Salle 5340 / * Monday, March 27, 2017, 4pm, Room 5340 *

In this talk, I will explain Nash's proof of his C^{1} isometric embedding theorem, one of the most striking examples of Gromov's h-principle. After illustrating the main ideas of the proof, I will discuss the question of rigidity and flexibility of
C^{1, α} isometric embeddings, first pioneered in the fities by Borisov and rediscovered more recently by Sergio Conti, László Székelyhidi and myself. Finally, I will draw a parallel between a problem of Gromov and the Onsager's conjecture.

## The Onsager's Theorem III [ Video ]

Le mardi 28 mars 2017, 16h00, Salle 5340 / * Tuesday, March 28, 2017, 4pm, Room 5340 *

In this talk, I will describe the main ideas of the first construction of energy-dissipative continuous solutions of the Euler equations, from my 2012 joint work with László Székelyhidi. I will then describe how such construction leads naturally to Hölder regularity and discuss the main obstacle in getting the sharp Hölder exponent.

## LIEU / VENUE

Salle / Room 6214 (le 24 mars, March 24)

Salle / Room 5340 (le 27 et 28 mars, March 27, 28)

Pavillon André-Aisenstadt

Université de Montréal

2920, chemin de la Tour

Le café sera servi ŕ 15h30 soit avant chaque conférence.

*Coffee will be served before each talk at 3:30 p.m.*