Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Workshop on Geometry of Lagrangian Grassmannians and nonlinear PDEs

created by moreno on 02 Feb 2016

5 sep 2016 - 9 sep 2016

Institute of Mathematics, PAN, Warsaw, Poland

A consistent geometric theory of nonlinear PDEs can obtained by using jet bundles and their natural structures. The so–obtained framework is part of a larger scheme, involving prolongations of contact manifolds, which allows to regard any PDE as a bundle of hypersurfaces in a isotropic Grassmannian manifold. In particular, second–order nonlinear PDEs correspond to hypersurfaces in the Lagrangian Grassmannian.

The workshop is based on the following three premises.

1) Lagrangian Grassmannians are interesting manifolds on their own, independently on their relationship with nonlinear PDEs: they display a rich intrinsic geometry, and their hypersurfaces can be studied through old and recent methods coming from unexpectedly distant areas.

2) There are important open problems concerning nonlinear PDEs, like those of obtaining (partial) classifications, or proving (non) equivalence theorems, which will clearly benefit from an appropriate geometric reformulation, not necessarily based on jet spaces or contact manifolds.

3) An important class of nonlinear PDEs, which occurs ubiquitously and transversally in very distant areas of Mathematics and Mathematical Physics, is that of integrable systems, i.e., systems of equations whose study is simplified by the presence of (nonlocal) symmetries and$/$or conservation laws. In spite of their importance, is not yet clear what is the correct, general and intrinsic geometric counterpart to the notion of integrability.

The workshop is aimed at clarifying these three points, through four three–hours mini–courses, to present some particular ongoing research in these directions, through four one–hour seminars, and to bring together experts with the necessary complementary skills to laid down effective and realistic plans for attacking unsolved problems.

Organizers: Jan Gutt, Gianni Manno, Giovanni Moreno.

Speakers: Ian Anderson (TBC), Gary Jensen, Emilio Musso, Francesco Russo, Abraham David Smith (TBC).

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