Ivan Solonenko (Stuttgart) will speak in the geometry seminar on Monday 4th November, at 2pm in the Salle des Profs (9th floor of building NO). Ivan’s title is “Classification of cohomogeneity-one actions on noncompact symmetric spaces” and his abstract is below.
The first systematic approach towards classifying isometric cohomogeneity-one actions on symmetric spaces of noncompact type dates back to the work of Berndt and Brück from 2001. Later on, in a series of articles, Berndt and Tamaru reduced the classification problem to an obscure and elaborate problem in the representation theory of reductive Lie groups, known as the nilpotent construction problem. Due to the complexity of that problem, the classification efforts have been at a virtual standstill since 2013. In this talk, I will report on the joint work with Víctor Sanmartín-López, in which we fully resolve the nilpotent construction problem, thus completing the classification of cohomogeneity-one actions on symmetric spaces of noncompact type. As a byproduct, I will give a descriptive structural result on transitive actions on such spaces, and I will also show how many natural classes of homogeneous minimal submanifolds in these spaces can be realized as solvsubmanifolds.