# Gaofeng Huang: Hamiltonian Carleman approximation for Calogero-Moser spaces

V torek, 8. oktobra ob 12. uri in 30 minut, bo v okviru seminarja za kompleksno analizo predaval Gaofeng Huang z Univerze v Bernu, Svica.

Title: Hamiltonian Carleman approximation for Calogero-Moser spaces.

Abstract: In 1927 Torsten Carleman showed that for the real line R in the complex plane C, smooth functions can be approximated on R by holomorphic functions restricted to R. The approximation holds on the entire real line which is in particular unbounded in C. Since then there are generalizations of Carleman-type approximation in various directions. In the special class of symplectic automorphisms in place of functions, Deng and Wold recently proved Carleman approximation for symplectic diffeomorphisms of R^2n onto itself by holomorphic symplectic automorphisms of C^2n which preserve the real part R^2n. There are two steps: first a local approximation, then the transfer of the local effect to a global one. In the local phase a key role is played by the symplectic density property. This property has been confirmed by Forstneric in the 90s for C^2n and lately by Andrist and the speaker for the Calogero-Moser space, which is a complex affine algebraic manifold endowed with a holomorphic symplectic form. The Calogero-Moser space can be seen as a completion of the phase space to a classical physical system, consisting of n particles on a line with pairwise inverse square potential. After properly choosing a totally real submanifold, we will see in this talk how to apply Deng and Wold’s techniques to Calogero-Moser spaces.

Predavanje bo potekalo hibridno, v predavalnici 3.05 na Jadranski 21 in preko aplikacije ZOOM:

https://uni-lj-si.zoom.us/j/93098854181

Meeting ID: 930 9885 4181

Vljudno vabljeni!

Vodji seminarja

Franc Forstneric in Barbara Drinovec Drnovsek