“An introduction to infinite-dimensional geometry in continuum mechanics”
Thursday 26 March 2026 h. 14:30 - Room 2BC30 - Francesca Berlinghieri (Padova, Dip. Mat.)
Abstract
Continuum mechanics studies the motion and deformation of bodies modeled as continuous media. It covers a large number of theories, including ideal, compressible and viscous fluid models, as well as linear and nonlinear elasticity.
In this talk, a transition from Newtonian mechanics of discrete systems to the setting of continuum mechanics will be presented through the principle of virtual works. Particular emphasis will be given to the role of the placement (or deformation) map as primary descriptor of the continuum. Such maps naturally belong to functional spaces that are inherently infinite-dimensional. This perspective motivates the study of the geometry of spaces of admissible deformations. As a classical example, we will briefly discuss the approach introduced by Arnold, and later developed by Ebin and Marsden, where the motion of an incompressible perfect fluid is interpreted as a geodesic flow on the (infinite-dimensional) Lie group of volume-preserving diffeomorphisms.
The video of the seminar will appear shortly afterwards in this Mediaspace channel.
