Recent

Folding papers and turbulent flows

Camillo De Lellis
University of Zürich
February 24, 2017
In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it, no matter how large it is. A couple of decades later Gromov showed how Nash's ideas can be used to reinterpret other known counterintuitive facts in geometry and to discover many new ones. Ten years ago László Székelyhidi and I discovered unexpected similarities with the behavior of some classical equations in fluid dynamics.

Symplectic homology for cobordisms

Alexandru Oancea
Université Pierre et Marie Curie; Member, School of Mathematics
February 23, 2017
Symplectic homology for a Liouville cobordism (possibly filled at the negative end) generalizes simultaneously the symplectic homology of Liouville domains and the Rabinowitz-Floer homology of their boundaries. I intend to explain a conceptual framework within which one can understand it, and give a sample application which shows how it can be used in order to obstruct cobordisms between contact manifolds. Based on joint work with Kai Cieliebak and Peter Albers.

Folding papers and turbulent flows

Camillo De Lellis
University of Zürich
February 23, 2017
In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it, no matter how large it is. A couple of decades later Gromov showed how Nash's ideas can be used to reinterpret other known counterintuitive facts in geometry and to discover many new ones. Ten years ago László Székelyhidi and I discovered unexpected similarities with the behavior of some classical equations in fluid dynamics.

Singularity formation in incompressible fluids

Tarek Elgindi
Princeton University
February 22, 2017
We discuss the problem of singularity formation for some of the basic equations of incompressible fluid mechanics such as the incompressible Euler equation and the surface quasi-geostrophic (SQG) equation. We begin by going over some of the classical model equations which have been proposed to understand the dynamics of these equations such as the models of Constantin-Lax-Majda and De Gregorio. We then explain our recent proof of singularity formation in De Gregorio's model.

Folding papers and turbulent flows

Camillo De Lellis
University of Zürich
February 21, 2017
In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it, no matter how large it is. A couple of decades later Gromov showed how Nash's ideas can be used to reinterpret other known counterintuitive facts in geometry and to discover many new ones. Ten years ago László Székelyhidi and I discovered unexpected similarities with the behavior of some classical equations in fluid dynamics.