Let G be a connected reductive algebraic group. A G-variety X is called a spherical variety if a Borel subgroup B of G has an open dense orbit in X. Then G has finitely many orbits in X, and one of them is open. This open orbit of G is of the form G/H, where H is an algebraic subgroup of G. A subgroup H of G for which G/H is spherical is called a spherical subgroup.

The problem of classification of spherical varieties reduces to the following two problems: classification of spherical subgroups H of G, and classification of spherical embeddings of G/H (that is, spherical varieties containing G/H as the open orbit of G). In 2017 we will concentrate on spherical homogeneous spaces.

Note that spherical embeddings are classified in terms of so-called colored cones and colored fans. This generalizes the classification of toric varieties using cones and fans.

Some knowledge of reductive and semisimple groups will be assumed. In the first meeting, a one hour crash course on reductive groups and root systems will be given.

Concerning links and texts on spherical varieties, more or less suitable for beginners, I can suggest the following:

Wikipedia page.
Perrin's survey.
Knop's paper.
Timashev's book.
Brion's preprint in French.
Luna's paper in French.
Gagliardi's M.Sc. thesis in German.
Borovoi's preprint.

Contact me at: borovoi@post.tau.ac.il. Please write in subject: Spherical varieties.

Seminar homepage: http://www.tau.ac.il/~borovoi/courses/Spherical/SV.html