Manchester Geometry Seminar 2013/2014

Thursday 12 December 2013. The Frank Adams Room (Room 1.212), the Alan Turing Building. 4.15pm

Monge-Ampère Equations, Their Invariants and (Generalised) Geometries

Vladimir Rubtsov (Université d'Angers)

The Monge-Ampère (MAE) equations are important 2nd order non-linear equations which appear in many domains of mathematics and mathematical physics --- from differential geometry of surfaces to so-called non-compact Calabi-Yau varieties and "non-cosmic" strings, problems of optimal mass transportation and the Mirror Conjecture.

In my talk I shall try to explain a geometric approach to this class of equations, which is based on some ideas and methods from contact and symplectic geometry. This approach leads not only to a possibility to solve (sometimes :) ) the MAE exactly, to find their symmetries and conservation laws but also provides a study of some interesting (classical and generalised) geometric structures.