Summer school I: Invitation to complex geometry
Description
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: Pluripotential theory and L∞ estimates for complex Monge-Ampère equations
Abstract: In these lectures, we introduce and explore fundamental concepts in pluripotential theory, which are essential for studying (degenerate) complex Monge-Ampère equations on Kähler manifolds. We then shift our focus to a novel approach for obtaining L∞ a priori estimates for these equations. This method, which has a "local" character and relies solely on the use of envelopes, was recently developed by Guedj and Lu.
Siarhei Finski: Asymptotic study of submultiplicative filtrations
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
Link to the registration page:
https://invite.ventla.io/erdos
Registration is open until: June 15, 2025
Note that acceptance to the school is not automatic. Although you may complete the registration process successfully, confirmation will be sent directly by the organizers within two weeks after receiving the required documents. The sooner you register, the better.
Please note that applications for financial support for accommodation are closed much earlier - see below. In the registration you should provide a url link with your cv including your list of publication (in case this is problematic, send the file directly to complex.geometry@renyi.hu, with the subject "invitation to complex geometry"). Students should also arrange for a short letter of recommendation to be sent to the email address complex.geometry@renyi.hu by a faculty member, preferably by the advisor/mentor. In your registration you can indicate that you are applying for financial support for accommodation. The school takes place during the top touristic season in Budapest, so accommodation prices can be expected to increase dramatically with time.
Pending support from the NSF, we expect to partially reimburse travel costs of participants from the US.
ACCOMMODATION
Limited financial support for accommodation is available for students and postdocs. Accommodation is provided in double and triple rooms (i.e. you must share your room with other participant(s) of the school).
Deadline for applications for financial support: April 30, 2025
Please note that those who are supported are expected to attend the whole event. Accommodation is normally supported for 6 nights (Sunday to Friday) at most. If you don't need financial support, but you would like our administration to help you with booking (at possible discounted prices), please write to the secretary of the Erdős center: Mrs. Ildikó Bogáti: bogati@renyi.hu
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):