- Series
- School of Mathematics Colloquium
- Time
- Thursday, March 2, 2023 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Boris Khesin – University of Toronto – khesin@math.toronto.edu – http://www.math.toronto.edu/khesin/
- Organizer
- Tom Kelly
Please Note: Live-stream link: https://gatech.zoom.us/j/93100501365?pwd=bWFEeURxek5pWG1BRjN4MHcvYllYQT09 Passcode provided in talk announcement
We describe a geometric framework to study Newton's
equations on infinite-dimensional configuration spaces of
diffeomorphisms and smooth probability densities. It turns out that
several important PDEs of hydrodynamical origin can be described in
this framework in a natural way. In particular, the so-called Madelung
transform between the Schrödinger-type equations on wave functions and
Newton's equations on densities turns out to be a Kähler map between
the corresponding phase spaces, equipped with the Fubini-Study and
Fisher-Rao information metrics. This is a joint work with G.Misiolek
and K.Modin.