Научный семинар Лаборатории алгебраической геометрии и ее приложений: Иван Солоненко, Kings College London (онлайн семинар)

На семинаре выступит Иван Солоненко (Kings College London) с докладом Hyperpolar homogeneous foliations on symmetric spaces of noncompact type

Аннотация: Due to their high degree of symmetry, Riemannian symmetric spaces are among the easiest classes of spaces to study, and so they provide a large testing ground for verification of various geometrical ideas and hypotheses. One of the most basic and fundamental projects in this area is to classify isometric actions of Lie groups on symmetric spaces. Unfortunately, this venture is overly hard and practically unfeasible. A more realistic idea would be to confine one’s attention to an easier subclass of actions which are manageable enough to allow classification. In this talk we will discuss several such subclasses that arise naturally, namely polar, hyperpolar, and cohomogeneity-one actions. Interestingly, symmetric spaces of noncompact type turn out to be significantly more complex than their compact counterparts in that regard, despite the duality between the two. After defining all the necessary objects and notions and looking at the (relative) easiness of the compact case, we will talk about hyperpolar actions on symmetric spaces of noncompact type all of whose orbits are principal and formulate a complete classification result. Time permitting, we will discuss the main ideas behind the proof and briefly mention the cohomogeneity-one case, where a complete classification of all actions is known.
It would be helpful if listeners had some acquaintance with Lie theory and homogeneous spaces.