BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Laura Geatti (Universita' di Roma Tor Vergata) DTSTART:20230913T160000Z DTEND:20230913T170000Z DTSTAMP:20260423T052836Z UID:VSGS/72 DESCRIPTION:Title: Ge ometry of Hermitian symmetric spaces under the action of a maximal unipote nt group.\nby Laura Geatti (Universita' di Roma Tor Vergata) as part o f Virtual seminar on geometry with symmetries\n\n\nAbstract\nGiven a compl ex manifold $M$ with a Lie group $G$ action by holomorphic transformatio ns\, \nit is of interest to understand associated invariant objects l ike the invariant Stein subdomains and the invariant plurisubharmoni c functions.\n\nA classical example of this framework is given by tube d omains in complex Euclidean space\, where $M={\\bf C}^n$ and $G={\\bf R}^ n$ acts by translations. \n\nAn ${\\bf R}^n$-invariant domain $D={\\bf R }^n+i\\Omega$ in ${\\bf C}^n$ is Stein if and only if its base $\\Omega$ is geometrically convex (Bochner's tube theorem). Moreover an ${\\bf R}^ n$-invariant function on a Stein tube domain $D$ is plurisubharmonic if an d only if its restriction to $\\Omega$ is convex. \n\n\n In this talk\, we present a generalization of the above results in the setting of a Herm itian symmetric space of the non-compact type $G/K$ under the action of a maximal unipotent subgroup $N\\subset G$. \nAs a by-product we obtain all $N$-invariant potentials of the Bergman metric of $G/K$ in a Lie theor etical fashion and an explicit formula for the moment maps $\\mu\\colon G/K\\to {\\mathfrak n}^*$ associated to such potentials.\n\n \nThis is wo rk in collaboration with Andrea Iannuzzi.\n LOCATION:https://researchseminars.org/talk/VSGS/72/ END:VEVENT END:VCALENDAR