2014 Theme Semester on Convex Integration and Analysis

Department of Mathematics, University of Pittsburgh
January - May 2014


The goal of the Semester is to expose graduate students, visitors and faculty to some important techniques and results in modern Mathematical Analysis, with an orientation towards Geometric Analysis and Convex Integration. The theory of Convex Integration originates in the work of Nash and Kuiper in 1950' where they showed that any given Riemannian manifold can be isometrically embedded in a Riemannian manifold of one higher dimension with a C^1-regular embedding. Later on, Gromov succeeded in resolving the same question in a more general framework of partial differential relations. Recently, new connections have been made between Convex Integration and Calculus of Variation, Fluid Mechanics, Microstructures and Nonlinear Elasticity.

The semester will consist of concentrated activities, including week-long five minicourses at graduate level, delivered by: V. Borelli, C. De Lellis, P. Lindqvist, A. Malchiodi and L. Szekelyhidi Jr. The Semester will also include a workshop "Advances in Nonlinear Analysis" in March 13-15, 2014.



Jan 20 - Jan 24, 2014
Professor Vincent Borrelli
Universite Lyon I, France

From convex integration to flat tori

Lecture 1: Tue 10am, 704 Thackeray Hall
Lecture 2: Wed 10am, 704 Thackeray Hall
Lecture 3: Th 10am, 704 Thackeray Hall
Lecture 4: Fri 10am, 704 Thackeray Hall


Feb 3 - Feb 7, 2014
Professor Peter Lindqvist
Norwegian University of Science and Technology

The infinity-Laplace equation

Lecture 1: Mon 10am, 704 Thackeray Hall
Lecture 2: Tue 10am, 704 Thackeray Hall
Lecture 3: Wed 10am, 704 Thackeray Hall
Lecture 4: Th 10am, 704 Thackeray Hall


March 3 - March 7, 2014
Professor Camillo De Lellis
University of Zurich, Switzerland

From Nash to Onsager, I

Lecture 1: Mon 10am, 704 Thackeray Hall
Lecture 2: Tue 10am, 704 Thackeray Hall
Lecture 3: Wed 10am, 704 Thackeray Hall
Lecture 4: Th 10am, 704 Thackeray Hall
Lecture 5: Fri 10am, 704 Thackeray Hall


March 24 - March 28, 2014
Professor Laszlo Szekelyhidi Jr.
University of Leipzig, Germany

From Nash to Onsager, II

Lecture 1: Mon 10am, 704 Thackeray Hall
Lecture 2: Tue 10am, 704 Thackeray Hall
Lecture 3: Wed 10am, 704 Thackeray Hall
Lecture 4: Th 10am, 704 Thackeray Hall


Apr 7 - Apr 11, 2014
Professor Andrea Malchiodi
University of Warwick, United Kingdom

Variational features of Liouville equations

Lecture 1: Mon 10am, 704 Thackeray Hall
Lecture 2: Tue 10am, 704 Thackeray Hall
Lecture 3: Wed 10am, 704 Thackeray Hall
Lecture 4: Th 10am, 704 Thackeray Hall
Lecture 5: Fri 10am, 704 Thackeray Hall


Funding for the Semester has been provided by the Mathematics Research Center at the University of Pittsburgh .

The poster can be downloaded by clicking on the image in the right hand side.

The organizing committee consists of: Piotr Hajlasz , Marta Lewicka , Juan Manfredi and Reza Pakzad .
Poster: