ICMS Seminar
The ICMS seminar aims to present and disseminate advances in different fields of the contemporary fundamental and applied mathematics, and to promote new cutting edge directions in Mathematics.
The ICMS seminar aims to present and disseminate advances in different fields of the contemporary fundamental and applied mathematics, and to promote new cutting edge directions in Mathematics. The seminar hosts scientific reports by collaborators and visitors of the ICMS, as well as colloquium-style lectures by invited speakers. The interdisciplinary features of the ICMS are reflected in the variety of topics covered in the seminar, ranging in algebraic and differential geometry, number theory, category theory, combinatorics, representation theory, mathematical physics, algebraic coding theory, etc. The venue is open to a wide audience, and the lectures are followed by time for interaction and discussion.
Seminar issues
Invariant theory, homogeneous projective varieties, and momentum maps, course by Valdemar Tsanov
After introducing the basic notions, I will derive some properties of momentum images related to fundamental forms and osculating varieties, as well as a lower bound on the minimal positive degree of a homogeneous invariant, derived using secant varieties. At the end I will present a class of homogeneous projective varieties, characterized by a special property of their secant varieties, where the relations between the above three concepts take a particularly pristine form.
Introduction to Projective Structures and Opers, course by Peter Dalakov
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.
About a generalisation of Sylvester’s law of inertia, talk by Stéphanie Cupit-Foutou
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
Numerical Calabi-Yau Metrics: An Informal Lecture by Michael R. Douglas
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.
Introduction to tensor triangular geometry
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.
