### Geometry and dynamics of compressible fluids

- Series
- School of Mathematics Colloquium
- Time
- Thursday, March 2, 2023 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Boris Khesin – University of Toronto – khesin@math.toronto.edu

**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.