Prof. Stéphanie Cupit-Foutou,
Title: Introduction to wonderful varieties
Abstract: Wonderful varieties were introduced by D. Luna as complete complex algebraic varieties sharing the main properties of De Concini-Procesi compactifications of adjoint groups or more generally of symmetric spaces.
In this series of lectures, I shall give a gentle introduction on wonderful varieties, starting with Luna's definition and a discussion on some concrete examples. Thereafter, I shall introduce spherical varieties and focus on their properties in order to explain the important role played by the wonderful varieties among the spherical varieties.
Prof. Dmitry Timashev,
Title: Spherical homogeneous spaces
Abstract: Spherical homogeneous spaces are a beautiful class of homogeneous spaces of reductive algebraic groups which include almost all classical examples such as: projective spaces, quadrics, Grassmannians, flag varieties, symmetric spaces, and more. A important feature of spherical homogeneous spaces is that they arise in different areas and are remarkable from different viewpoints including equivariant algebraic geometry, representation theory and harmonic analysis, symplectic geometry and integrable systems, Schubert calculus and enumerative geometry, etc.
In my lectures, I shall introduce spherical homogeneous spaces from various viewpoints and consider basic examples. I plan to discuss several algebraic and representation-theoretic applications of spherical homogeneous spaces. If time allows I shall give an introduction to our work in progress with Stephanie Cupit-Foutou on spherical homogeneous spaces over real numbers, especially on classification of real orbits in their real loci.