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.
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.
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.
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.
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.
An integer partition of an integer number n is simply a decreasing sequence of integers whose sum is equal to n. Naturally, integer partitions and their theory are ubiquitous in mathematics. I will report on a link between an algebro-geometric invariant of singularities and the theory of integer partitions in the spirit of Ramanujan. The talk is aimed at a wide audience of mathematicians.
Michael R. Douglas received his PhD in Physics in 1988 under the supervision of John Schwarz, one of the developers and leading researchers in superstring theory. Douglas is best known for his work in string theory, for the development of matrix models (the first nonperturbative formulations of string theory), for his work on Dirichlet branes and on noncommutative geometry in string theory, and for the development of the statistical approach to string phenomenology. He has influenced the developments of modern mathematics by finding interpretations of branes on the language of derived categories and introducing the theory of stability conditions for categories.
In the first part of the talk, I shall explore the consequences of distinguishing the foundations of meaning and the foundations of truth in mathematical statements, or imagination and rigor as motors of mathematical development. The foundations of meaning can be sought in our largely unconscious perception of the world, which modern cognitive science is exploring.
The event is jointly organized by the International Centre for Mathematical Sciences (ICMS-Sofia) at the Institute of Mathematics and Informatics in Sofia, and the Institute for the Mathematical Sciences of the Americas (IMSA) at the University of Miami. The conference will be held at the UM campus.