11 08, 2023

Remarks on Hodge Polynomials for Certain Non-algebraic Complex Manifolds, by Ernesto Lupercio

2023-08-31T14:14:48+03:00August 11th, 2023|Consortium Distinguished Lecture Series, News|

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.

11 08, 2023

Borel-Weil Theorem and Laplace eigenfunctions on Riemannian symmetric spaces, by Gueo Grantcharov

2023-08-31T14:12:58+03:00August 11th, 2023|Consortium Distinguished Lecture Series, News|

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.

9 08, 2023

Period mappings for anti-canonical pairs, by Phillip Griffiths

2023-08-11T14:26:11+03:00August 9th, 2023|Consortium Distinguished Lecture Series, News|

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.

9 08, 2023

The generazed Calabi-Yau problem, by Vestislav Apostolov

2023-08-09T10:57:36+03:00August 9th, 2023|Consortium Distinguished Lecture Series, News|

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.

27 06, 2023

Introduction to tensor triangular geometry

2023-06-27T10:49:08+03:00June 27th, 2023|ICMS Seminar, News|

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.

30 05, 2023

Arc spaces and partition identities

2023-05-30T13:05:43+03:00May 30th, 2023|Colloquium, News|

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.

22 05, 2023

Consortium Distinguished Lecture Series presents Michael R. Douglas

2023-06-27T10:36:14+03:00May 22nd, 2023|Consortium Distinguished Lecture Series, News|

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.

9 05, 2023

Objectivity and Subjectivity in Mathematics

2023-05-09T15:41:59+03:00May 9th, 2023|ICMS Seminar, News|

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.

30 04, 2023

Quantum Toric Geometry, Generalized Geometries and O-Minimality

2023-05-09T15:46:55+03:00April 30th, 2023|Conferences, News|

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.

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