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
Remarks on Hodge Polynomials for Certain Non-algebraic Complex Manifolds, by Ernesto Lupercio
This two talks explore Hodge polynomials and their properties, specifically focusing on non-Kähler complex manifolds. We investigate several families of such manifolds, including (Quasi) Hopf, (Quasi) Calabi-Eckmann, and LVM manifolds, alongside a class of definable complex manifolds that encompasses both algebraic varieties and the aforementioned special cases. Our main result establishes the preservation of the motivic nature of Hopf polynomials inside this broader context.
Borel-Weil Theorem and Laplace eigenfunctions on Riemannian symmetric spaces, by Gueo Grantcharov
In this talk I'll present a geometric relation between the Laplace-Beltrami spectra and eigenfunctions on compact Riemannian symmetric spaces and the Borel-Weil theory using ideas from symplectic geometry and geometric quantization.
Period mappings for anti-canonical pairs, by Phillip Griffiths
Anti-canonical pairs (Y, D) are logarithmic K3 surfaces. It is well known that they have a rich geometry. A recent result, whose proof was motivated by mirror-symmetry, establishes a conjecture by Looijenga giving conditions for smoothability of the cusp obtained by contracting D. A central ingredient in the proof is a global Torelli theorem using the mixed Hodge structure on H2(Y −D). In this talk we will formulate and sketch the proof of this result.
The generazed Calabi-Yau problem, by Vestislav Apostolov
I will describe an extension, proposed by Hitchin and Gualtieri, of the notion of a Calabi-Yau structure to generalized Kähler geometry. I will then discuss a conjectural classification of the generalized Kähler Calabi-Yau geometries, expressed in terms of Bogomolov-Beauville decomposition, and present a partial resolution.
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.
