Workshop on Transformation Groups

In honor of Peter Heinzner

 

 

July 18^th, 2025 at Ruhr-Universität Bochum

 

 

Speakers

 

Leonardo Biliotti (Parma)

Jürgen Hausen (Tübingen)

Gerald Schwarz (Brandeis)

 

 

Venue

All talks will take place in IA 01/473. A campus map can be found here

 

 

Titles and abstracts

 

Leonardo Biliotti	Stability, analytic stability for real reductive Lie groups
	In this talk, we study the action of a real reductive group G on a real submanifold X of a Kähler manifold Z. We assume that the action of G extends holomorphically to an action of a complex reductive group and is Hamiltonian with respect to a compatible maximal compact subgroup of the complex group. There is a corresponding gradient map arising from a Cartan decomposition of G. Under mild assumptions on the G-action on X, we characterize the G-orbits in X that intersect the zero level set of the gradient map in terms of the maximal weight functions. If time permits, we also study the natural G-action on the space of probability measures on X. We define an analogue of the gradient map and the usual concepts of stability, proving numerical criteria for stability, semi-stability, a polystability. The result are proved in collaboration with Oluwagbenga Joshua Windare. In the classical case of a group action on a Kahler manifold these characterizations are due to Mundet i Riera, Teleman, Kapovich, Leeb and Millsos and probably many others. In fact many of these ideas go back as far as Mumford.
Jürgen Hausen	Title
	Abstract
Gerald Schwarz	Title
	Abstract

 

 

 

Schedule

 

11:00	Welcome by the Dean
11:30 - 12:20	Jürgen Hausen:
Lunch break
14:00 - 14:50	Leonardo Biliotti: Stability, analytic stability for real reductive Lie groups
Coffee break
15:30 - 16:20	Gerald Schwarz:

 

Talks will take place in IA 01/473.

 

 

 

Organisers

 

Stéphanie Cupit-Foutou (Bochum)

Daniel Greb (Essen)

Christian Miebach (Calais)

Stefan Nemirovski (Wuppertal)

 

 

Financial support

The workshop is supported by CRC/TRR 191 Symplectic Structures in Geometry, Algebra and Dynamics.