Summer school I: Invitation to complex geometry

The Summer school: "Invitation to complex geometry" will be held between 04-08 August 2025 at the main lecture hall of the Rényi Institute (Budapest) as part of the thematic semester Complex analysis and Geometry (August-December 2025) hosted by the Erdős center. Graduate students (Msc and PhD), postdocs, and early career researchers are encouraged to apply. 

MINICOURSES

During this one week summer school, Eleonora di Nezza (Paris, Sorbonne) and Siarhei Finski (Paris, CNRS) will give introductory talks on Kähler geometry, highlighting recent advances, to a group of non-experts, primarily composed of students and postdocs.

Eleonora Di Nezza: Geodesics in the space of Kähler potentials

Tutor: Chung-Ming Pan

Abstract: A central problem in Kähler geometry is the search for canonical metrics. One powerful method for approaching this problem is the variational approach, which involves studying a suitable functional defined on an infinite-dimensional space, whose critical points correspond to the desired metrics.
Motivated by this framework, these lectures focus on the infinite-dimensional space of Kähler potentials, denoted by \mathcal{H}. We begin by studying geodesics in $\mathcal{H}$, introducing a family of distances  $d_p​$, and showing that geodesics minimize these distances. Our final goal is to understand the metric completions of  $ \mathcal{H}$ with respect to the distances  $d_p$​.

Siarhei Finski: Asymptotic study of submultiplicative filtrations

Tutor: Wei-Chuan Shen

Abstract: It has long been recognized that the study of manifold degenerations plays a crucial role in addressing many questions in geometry, including the search for canonical metrics. Some degenerations can be understood on the algebraic level through the so-called submultiplicative filtrations, which are certain filtrations on rings respecting the algebraic structure. The most basic example is the filtration on the space of homogeneous polynomials given by the order of vanishing along a subvariety in the projective space.

This course is about the geometric quantization approach to these filtrations, which effectively establishes several results at the crossroads of algebraic and differential geometry. We discuss some applications towards the search of canonical metrics and cover the necessary preliminaries including the Ohsawa-Takegoshi extension theorem, Bergman kernels, and the theory of graded normed algebras.

REGISTRATION

The registration period has ended.

Limited financial support for accommodation is available for students and postdocs. 

LOCAL EXPENSES

Apart from the above support in accommodation, we cannot cover local expenses.

IMPORTANT INFORMATION

The conference organizers do not authorize any external subjects to arrange or propose accommodation for the participants. If you receive e-mails from travel or housing agencies, etc., containing booking offers and requests for sending your personal data or advance payment, you should treat them as scams.

All official communications will only come from the Erdős Center secretary or directly from the organizers. Those who requested financial support for the accommodation will get the details directly from the secretary of the Erdős Center.

Venue:  Main Lecture Hall, Rényi Institute

https://maps.app.goo.gl/RxdVNyhTAYXbzS2V8

The following link gives practical information (e.g. local traveling):

https://erdoscenter.renyi.hu/practicalities

Schedule

The schedule of the summer school and the lightning talks are available in Downloads below.