What is... geometric mechanics? (Antonio Michele Miti, Geometry section)

By Antonio Michele Miti (Geometry section)

Abstract. 

Geometric mechanics is a branch of mathematics applying differential geometry methods to many areas of mechanics, from the dynamics of point-particles to continuous media.

In this talk, we review the three cornerstones of this discipline - phase space, observables and symmetries- focussing on the centrality of the notion of symplectic forms. If time permits we will also discuss a possible generalization of the latter notion, named multisymplectic structure, that can be useful to encode mechanical systems with infinite degrees of freedom in a finite-dimensional setting.

The crucial message is that, just as geometry provide an intuition of how mechanical systems evolve, mechanics provides a context for interpreting many abstract differential geometry objects.

This PhD Colloquium takes place on line. All master students following the PhD Colloquium in the context of the Student Seminar in Mathematics will find the link to the on line seminar in the Toledo page of the Student Seminar in Mathematics. All staff members of the Department of Mathematics will receive the link to the on line seminar via e-mail a few days before the seminar. Other interested people may contact Bram Verjans to obtain the link.