Nash's C^1 Isometric Embedding Theorem and the Borisov-Gromov Prob..(Lecture 3) by Camillo De Lellis

Infosys-ICTS Ramanujan Lectures: The Onsager Theorem and Beyond

Speaker: Camillo De Lellis (Institute for Advanced Study, Princeton, USA)
Date & Time: 26 September 2024 to 03 October 2024
Venue: Ramanujan Lecture Hall, ICTS Bengaluru

Lecture 3
Date and time: 30 September 2024, 11:00 -12:30
Title: Nash's C^1 isometric embedding theorem and the Borisov-Gromov problem.
Abstract: In this lecture I will explain the ideas of Nash's surprising construction, in the 1950s, of many C^1 isometric embeddings of Riemannian manifolds as hypersurfaces of the Euclidean space. We will then touch upon an open problem in the area, due to to Borisov and Gromov, about the threshold Hoelder regularity for which the Nash phenomenon is possible. This problem turns out to be intimately linked to the Onsager conjecture and we will survey the results proved so far about it.

About the speaker:

Camillo De Lellis was born in 1976 in San Benedetto del Tronto, Italy. After earning his undergraduate degree in mathematics at the University of Pisa in 1999, he wrote his doctoral dissertation in 2002 under the supervision of Luigi Ambrosio at the Scuola Normale Superiore di Pisa. He joined the faculty of the University of Zürich in 2004 as Assistant Professor of Mathematics, and he was appointed Full Professor in 2005. In 2018 he moved to the Institute for Advanced Study in Princeton, where he holds the IBM von Neumann Professorship. He is active in the fields of calculus of variations, geometric measure theory, hyperbolic systems of conservation laws and fluid dynamics. He has been a plenary speaker at the European Congress of Mathematics at Krakow in 2012 and is a member of the Academia Aeuropea, of the German Academy of Sciences, and of the American Academy of Arts and Sciences. He is the recepient of the 2009 Stampacchia Medal, 2013 SIAG/APDE Prize (jointly with La'szlo' Sze'kelyhidi Jr.), 2013 Fermat Prize (jointly with Martin Hairer), 2014 Caccioppoli prize, 2015 Amerio Prize, 2020 Bocher Prize (jointly with Larry Guth and Laure Saint-Raymond), 2020 Feltrinelli prize, and 2021 Myriam Mirzakhani prize.

This lecture series is part of the program "Deterministic and Stochastic Analysis of Euler and Navier-Stokes Equations"