July 28 to August 3, 2024
Summer School on Geometric Analysis
and PDEs
in Będlewo, Poland
Embedded Files
Summer School on Geometric Analysis
Speakers & courses
Speakers & courses
Daniel Faraco (Universidad Autónoma de Madrid)
Staircase laminates, elliptic equations and Magnetic Helicity
The course will start with an introduction to the geometric aspects of compensated compactness and convex integration. The second part will focus on the various exotic laminates found in the literature, namely the Tn configuration and staircase laminates. We will then transition to applications, beginning with the regularity of quasiconformal mappings and solutions to quasilinear equations. The final part of the course will delve into the description of magnetized fluids, such as those found in tokamaks and sunflares. Here, we will explore how the density of magnetic helicity resembles the structure of the Jacobian determinant of quasiconformal maps. To wrap up the course, we will tie everything together by demonstrating how staircase laminates offer critical solutions regarding the conservation of magnetic helicity.
Lecture notes with exercises at the end
This course will focus on geometric inequalities — particularly isoperimetric inequalities and inequalities for PDE-driven shape functionals such as the Faber Krahn inequality. We will introduce some quantitative stability estimates, both classical and more contemporary, and discuss how these estimates can be applied in various mathematical settings.
Lecture 1: lecture notes and exercises
Lecture 2: lecture notes and exercises
Lecture 3: lecture notes and exercises
Felix Otto (Max Planck Institute for Mathematics in the Sciences in Leipzig)
A variational regularity theory for optimal transportation, and application to the matching problem
In this mini-course, we shall explain the variational approach to regularity theory for optimal transportation. As a text material, we refer to the lecture notes arXiv:2303.14462.
The advantage of this approach lies in its robustness, which allows to apply it to the optimal matching problem. For an introduction of the latter, see my recorded lectures under “From combinatorics to partial differential equations”.
Schedule
Schedule
schedule-new.pdfThe first lecture begins on Monday at 9:00 am, and the last lecture concludes on Friday at 5:30 pm. Bus transportation from Poznań to Będlewo will be scheduled for Sunday at 6:30 pm (see How to get there). Two organized transports from Będlewo will be available: one on Friday evening and the other on Saturday morning. If someone plans to arrive or depart at different hours, they will need to arrange transportation on their own.
Conference photos
Conference photos
The conference photo was taken on July 30th, and the second photo is from the kayaking trip on July 31st. To see them in full resolution, open in a new card. Thank you for being here!
Registration
Registration
In order to register, please fill out this form.
Registration closes June 30th, 2024. If you wish to apply for financial support, the deadline is April 30th, 2024.
Poster session
Poster session
All participants are welcome to contribute to the poster session. More details will be available later.
Activities
Activities
There will be additional activities meant to help in getting to know each other. More details will be available later.
A kayaking trip down the river Warta will be organized on Wednesday afternoon.
A bonfire will be held on one of the evenings.
We also encourage everyone to take advantage of the pleasant neighborhood (Wielkopolski National Park) in their free time. For example, it is possible to get a swim in Dymaczewskie lake, a walking distance from the venue.
Organizers & contact
Organizers & contact
Anna Zatorska-Goldstein (University of Warsaw)
Katarzyna Mazowiecka (University of Warsaw)
Michał Miśkiewicz (University of Warsaw)
Aneta Wróblewska-Kamińska (Institute of Mathematics PAS)
Contact: 24-summersogaapdes@impan.pl
Venue
Venue
ul. Parkowa 1
62-061 Będlewo
Poland
Będlewo Conference Center is part of the Institute of Mathematics of the Polish Academy of Sciences (IM PAN) and its Banach Center. Besides standard conference facilities, it offers discussion rooms with blackboards and flip charts, and it has a fitness room, a bar, a 24h reception desk, and free parking. All rooms have private bathrooms.
The conference center is located in a XIX century neo-gothic palace, surrounded by a huge park.
How to get there
How to get there
General arrival instruction can be found here. The conference fee covers bus transfers:
From Poznań to Będlewo: on Sunday evening (July 28th, ~6.30 PM)
From Będlewo to Poznań: on Friday evening (August 2nd, ~5.45 PM) or on Saturday after breakfast (August 3rd, ~9.00 AM)
The meeting point for the bus is so-called Dworzec Letni located outside the railway station. Be careful because the railway station in Poznań has a non-intuitive structure and you can get lost quickly - follow the directions on the following maps and look for the note Conference Będlewo.
Conference fee
Conference fee
The conference fee is 1200 PLN or 280 EUR or 300 USD, paid to one of the bank accounts below. It covers accommodation (mostly in double rooms) with full day meals, as well as bus transfers between Poznań and the Będlewo Conference Center. There is funding available – during registration it is possible to apply for a waive of the conference fee. The deadline for application for financial support is April 30th, 2024.
Please include the full name of the participant and the word "SGAPDE2024" in the title of your transfer.
Payment details:
PLN: PL 48 1130 1017 0020 1467 1520 0002
EUR: PL 80 1130 1017 0020 1467 1520 0008
USD: PL 37 1130 1017 0020 1467 1520 0006
BIC/SWIFT: GOSKPLPW
Bank name: Bank Gospodarstwa Krajowego, Aleje Jerozolimskie 7, 00-955 Warszawa
Account owner: Instytut Matematyczny PAN, Warszawa, Śniadeckich 8
Funding
Funding
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