Thursday, September 3rd, 2026
Program Talk: Boris Khesin
Time: 11:15 AM - 12:15 PM
Location: SCGP 313
Title: Madelung hydrodynamics and Poisson geometry of wave functions
Speaker: Boris Khesin
Abstract: We describe the Poisson geometry of the Madelung transform between quantum mechanics and hydrodynamics for generic wave functions. It turns out that for arbitrary oriented manifolds this transform, being regarded as a momentum map, naturally defines prequantum bundles for coadjoint orbits of semidirect extensions of diffeomorphism groups. Furthermore, we show that the Madelung framework provides a natural infinite-dimensional version of the convexity results for Hamiltonian torus actions, thus giving a partial answer to Atiyah's question.
Title: Madelung hydrodynamics and Poisson geometry of wave functions
Speaker: Boris Khesin
Abstract: We describe the Poisson geometry of the Madelung transform between quantum mechanics and hydrodynamics for generic wave functions. It turns out that for arbitrary oriented manifolds this transform, being regarded as a momentum map, naturally defines prequantum bundles for coadjoint orbits of semidirect extensions of diffeomorphism groups. Furthermore, we show that the Madelung framework provides a natural infinite-dimensional version of the convexity results for Hamiltonian torus actions, thus giving a partial answer to Atiyah's question.