tbranzov

A complex projective structure on a Riemann surface is determined by an atlas, whose transition functions are Moebius (fractional-linear) transformations. There are multiple   descriptions of these structures: as certain flat PGL_2-bundles, as Sturm-Liouville operators, as holomorphic connections on the (first) jet bundle of the dual of a theta-characteristic, etc. This mini-course is an introduction to the fundamentals of projective structures, accessible to students and non-specialists. We will also explore links to some classical geometric objects (such as quadratic differentials and Schwarzian derivatives), as well as some generalisations (G-opers) introduced by Beilinson and Drinfeld.

Sylvester’s law of inertia can be formulated in terms of group actions when considering real linear groups acting on real quadratic forms by base change. After reviewing this celebrated result from this perspective, I will give a generalisation of it in the setting of so-called spherical varieties (a class of complex varieties including flag varieties, toric varieties, symmetric spaces, etc.). This is a joint work with D. Timashev

We look forward to welcoming you to ICMS-Sofia on June 29, 2023, at 13:00 (EEST, Sofia time) for an enlightening exploration of Numerical Calabi-Yau Metrics.

In a series of four talks, I will try to give a brief introduction to the subject and look at examples and applications following the exposition of universality, functoriality and localization, and triangulated categories and localization. The main references on the subject are the tensor triangulated categories and the Balmer spectrum and some examples and applications.