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

Cette conférence s'adresse à 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 C¹ 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)

Centre de recherches mathématiques
Pavillon André-Aisenstadt
Université de Montréal
2920, chemin de la Tour

Le café sera servi à 15h30 soit avant chaque conférence.
Coffee will be served before each talk at 3:30 p.m.

Camillo De Lellis

BIOGRAPHIE

Camillo De Lellis est professeur de mathématiques à l'Université de Zürich. Il a reçu son doctorat en 2002 à la Scuola Normale Superiore di Pisa sous la supervision de Luigi Ambrosio. M. De Lellis a apporté une contribution remarquable au calcul des variations, à la théorie de la mesure géométrique, aux dynamiques des fluides et aux systèmes de lois de conservation. Il a particulièrement obtenu des résultats significatifs conjointement avec László Székelyhidi sur les solutions dissipatives des équations incompressibles de Euler. En reconnaissance de son travail, Camillo De Lellis a reçu de nonmbreux honneurs tels que la médaille Stampacchia en 2009 , une invitation comme conférencier au ICM 2010 de Hyderabad, le prix Fermat en 2013 et le prix Caccioppoli en 2014.

BIOGRAPHY

Camillo De Lellis is Professor of Mathematics at University of Zürich. He received his PhD in 2002 at the Scuola Normale Superiore di Pisa under the supervision of Luigi Ambrosio. Professor De Lellis has made remarkable contributions in calculus of variations, geometric measure theory, fluid dynamics and systems of conservation laws. In particular, together with László Székelyhidi, he has obtained significant results on Onsager’s conjecture about dissipative solutions to the Euler incompressible equations. In recognition of his work, Camillo De Lellis has received numerous awards such as the 2009 Stampacchia medal, an invitation to speak at the 2010 ICM in Hyderabad, the 2013 Fermat Prize, and the 2014 Caccioppoli Prize.