Consortium Distinguished Lecture Series

14 11, 2023

Bubbling symplectic structures on moduli, a talk by Tony Pantev

2023-11-20T17:05:44+02:00November 14th, 2023|Consortium Distinguished Lecture Series, News|

 I will describe a new geometric method for constructing and controlling shifted symplectic structures on the moduli of vector bundles along the fibers of a degenerating family of Calabi-Yau varieties. The method utilizes bubbling modifications of the boundaries of limiting moduli spaces to extend the symplectic structure on the general fiber to a relative symplectic structure defined on the whole family. As a proof of concept we show that this produces a universal relative symplectic structure on the moduli of Gieseker Higgs bundles along a semistable degeneration of curves. We also check that the construction works globally over the moduli stack of stable curves and show that the Hitchin map has the expected behavior in the limit. This is a joint work with Oren Ben-Bassat and Sourav Das.

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.

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.

17 01, 2023

Consortium Distinguished Lecture Series – Andrés Navas

2023-01-17T09:26:19+02:00January 17th, 2023|Consortium Distinguished Lecture Series, News|

Andrés Navas is a mathematician specializing in dynamical systems, geometry, and group theory and is a world-renowned expert in ergodic theory. He was a student of Étienne Ghys. For his scientific achievements, he was awarded the MCA prize.

18 07, 2022

Ernesto Lupercio – Self-organized Criticality and Artificial Life

2022-07-22T11:40:54+03:00July 18th, 2022|Consortium Distinguished Lecture Series, News|

In this series of talks, we will explore how the field of self-organized criticality is useful to inform the structure of artificial models of life. This is joint work with Kalinin, Tabares and Shkolnikov, and with Cruz, Muñoz and Viafara.

25 05, 2022

Ernesto Lupercio – Localization Methods for Orbifolds and Motivic Integration

2022-07-18T13:36:09+03:00May 25th, 2022|Consortium Distinguished Lecture Series, News|

ICMS-Sofia and IMSA-Miami present the next part of the Consortium Distinguished Lecture Series. Prof. Ernesto Lupersio (CINESTAV) will talk on Localization Methods for Orbifolds and Motivic Integration. The series will be on May 26-27, 2022, 19:00 (EEST, Sofia time), via Zoom.

18 04, 2022

Functional Inequalities and Improvements: Stability

2022-07-18T13:39:11+03:00April 18th, 2022|Consortium Distinguished Lecture Series|

Functional inequalities constitute a very useful toolbox in various fields of Mathematics, like analysis, spectral analysis, mathematical physical, theory of partial differential equations and differential geometry. For each of them, knowing the best constant in the inequality and as much as possible about the extremal, optimizing, functions is very important. In these presentations I will describe how this field has developed very strongly in the last decades and how now we dispose of a good set of strategies to address all the above issues for a large family of inequalities. Also a recent set of important results are devoted to the improved inequalities that can be written for non optimizers, topic which is denoted as “stability” for the inequalities. The methods that one can use and the different results that have been obtained will be discussed via the choice of a set of particular inequalities which enjoy interesting features or that are very useful in particular applications.

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