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conference
27/03/2023 31/03/2023

PDE tasting

This intensive mini-course is aimed at undergraduate students of mathematics with a solid foundation of analysis and measure theory (background in PDE is not essential). The goal is to give a tasting of some of the great problems in mathematical fluid mechanics, from the perspective of the analysis of partial differential equations, focusing on the most basic models: the incompressible Euler and Navier-Stokes equations.

  • Why is Jupiter's great red spot so stable that it has been observed for over 100 years, and how to explain the emergence of such coherent structures? Is this an example of self-organized dynamics?
  • The butterfly effect of Lorenz in the case of chaotic finite-dimensional dynamical systems is well known. But Lorenz also predicted a much more catastrophic lack of determinism, the "real" butterfly effect: no matter how precise our measurements, we cannot predict the future of dynamical systems with "many" degrees of freedom.
  • It was observed by Mandelbrot that turbulent flows exhibit fractal-like structures. Can such structures really arise as solutions of a PDE and how to interpret this?
  • One of the 7 millenium prize problems is the question of singularity formation for the incompressible Navier-Stokes equations, or, simply stated: can water spontaneously explode? There are many other PDEs where singularity formation is interesting, so what makes the 3D Navier-Stokes equations so special (and the question so hard) that one puts a one-million dollar bounty on it?


The organizers of the School will take care of the accommodation of all the participants in Leipzig, of the morning and afternoon tea/coffee breaks as well as lunches during the days of the School.

The registration is closed.

Program

Mar 27, 2023
09:30 - 10:00
10:00 - 12:00 László Székelyhidi (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)
12:00 - 13:00
13:00 - 15:00 Balázs Maga (Hungarian Academy of Sciences, Budapest, Hungary), Jószef Kolumbán
15:00 - 16:00
16:00 - 17:00
Mar 28, 2023
09:30 - 10:00
10:00 - 12:00 László Székelyhidi (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)
12:00 - 13:00
13:00 - 15:00 Balázs Maga (Hungarian Academy of Sciences, Budapest, Hungary), Jószef Kolumbán
15:00 - 16:00
16:00 - 17:00
Mar 29, 2023
09:30 - 10:00
10:00 - 12:00 László Székelyhidi (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)
12:00 - 13:00
13:00 - 15:00 Balázs Maga (Hungarian Academy of Sciences, Budapest, Hungary), Jószef Kolumbán
15:00 - 16:00
16:00 - 17:00
Mar 30, 2023
09:30 - 10:00
10:00 - 12:00 László Székelyhidi (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)
12:00 - 13:00
13:00 - 15:00 Balázs Maga (Hungarian Academy of Sciences, Budapest, Hungary), Jószef Kolumbán
15:00 - 16:00
16:00 - 17:00
Mar 31, 2023
09:30 - 10:00
10:00 - 12:00 László Székelyhidi (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)
12:00 - 13:00
13:00 - 15:00 Balázs Maga (Hungarian Academy of Sciences, Budapest, Hungary), Jószef Kolumbán
15:00 - 16:00
16:00 - 17:00

Participants

Komálovics Ábel

Budapest University of Economics and Engineering, Hungary

Sebastian Bürger

Leipzig University, Germany

Barnabás Gárgyán

University of Szeged, Hungary

Villő Glavosits

University of Szeged, Hungary

Lukas Hauger

Max-Planck-Institute for Mathematics in the Sciences, Germany

Gergely Jakovác

Eötvös Loránd University, Budapest, Hungary

Áron Jánosik

Eötvös Loránd University, Budapest, Hungary

Zoltán Kalocsai

Eötvös Loránd University, Budapest, Hungary

Anett Kocsis

Eötvös Loránd University, Budapest, Hungary

Mátyás Kocsis

University of Debrecen, Hungary

Donát Ákos Köller

Budapest University of Technology and Economics, Hungary

József Kolumbán

Budapest University of Technology and Economics

Sam G. Krupa

Max Planck Institute for Mathematics in the Sciences, Germany

Balázs Maga

Hungarian Academy of Sciences, Hungary

Bence Mátravölgyi

Eötvös Loránd University, Budapest, Hungary

Csenge Miklós

Eötvös Loránd University, Budapest, Hungary

Zsófia Mikulás

Eötvös Loránd University, Budapest, Hungary

Harahm Park

Oxford University, United Kingdom

Orsolya Paróczi

Eötvös Loránd University, Budapest, Hungary

Sandra Ried

Leipzig University

Gabriel Sattig

Max Planck Institute for Mathematics in the Sciences

Olivér Sokvári

Eötvös Loránd University, Budapest, Hungary

László Székelyhidi

Max Planck Institute for Mathematics in the Sciences, Germany

Bálint Morgan Szilasi

University of Szeged, Hungary

Scientific Organizers

Balázs Maga

Hungarian Academy of Sciences

László Székelyhidi

Max Planck Institute for Mathematics in the Sciences

József Kolumbán

Budapest University of Technology and Economics

Administrative Contact

Anne Dornfeld

Max Planck Institute for Mathematics in the Sciences Contact via Mail