# Alexander Tumanov: A bounded pseudoconvex domain in C^n whose group of all biholomorphic automorphisms is the universal cover of SL(2,R)

V SREDO, 31. maja ob 14. URI in 15 MINUT, bo v okviru seminarja za kompleksno analizo predaval prof. Alexander Tumanov z University of Illinois at Urbana-Champaigne, ZDA.

Title: A bounded pseudoconvex domain in C^n whose group of all biholomorphic automorphisms is the universal cover of SL(2,R).

Abstract: For a bounded domain D in C^n, the group Aut(D) of all biholomorphic automorphisms of D is a finite dimensional real Lie group. Is the converse true? Bedford and Dadok (1987) and Saerens and Zame (1987) proved that every compact Lie group G can be realized as Aut(D) for a bounded strongly pseudoconvex domain D in C^n. When the group G is not necessarily compact, Shabat and Tumanov (1990) proved that every connected linear Lie group G can be realized as Aut(D), where D is a possibly unbounded strongly pseudoconvex domain in C^n of bounded type. When the group G is not necessarily linear, Winkelman (2004) and Kan (2007) proved that G can be realized as Aut(D), where D is a hyperbolic Stein manifold. The question whether D can be chosen as a bounded domain in C^n remained open so far. We prove the result for the simplest example of a non-linear Lie group, the universal cover of SL(2,R). This work is joint with George Shabat.

Predavanje bo potekalo hibridno, v PLEMLJEVEM SEMINARJU na Jadranski 19 in preko aplikacije Zoom:

https://uni-lj-si.zoom.us/j/94049045946?pwd=T3VxZHMvY3JlaUFlVXYrSlg0Wm5zZz09

Meeting ID: 940 4904 5946 Passcode: 723320

Vljudno vabljeni!

Vodji seminarja

Franc Forstneric in Barbara Drinovec Drnovsek