• September 30th, 2021 There has been another change of today's schedule. (If you don't see the version of today, please refresh (F5) the browser while viewing the schedule.)
• September 29th, 2021 Unfortunately, we had to slightly change the schedule of today and tomorrow. (If you don't see the version of today, please refresh (F5) the browser while viewing the schedule.)
• September 24th, 2021 We provide a booklet with further information (for this link you need to login with the credentials we had send around). Please have a look into it.
• September 21st, 2021 We have send around via the mailing list the credentials for accessing the internal event's webpage, which contains the needed information for joining the online meeting via zoom.
• September 8th, 2021 Have a look into the schedule for this event.
• August 25th, 2021 One month left and the summer school will start. Updates to this summer school will follow now more regularly on this webpage or via e-mail to the registered paerticipants.
• July 5th, 2021 We are extending the registration deadline to July 18th, 2021. 
• May 3rd, 2021 We are happy to announce that we will organize a summer school again. We are hoping and planning that it will be onsite. But we may change to a hybrid or even online only event.

This summer school is directed to PostDocs, PhD and advanced master students with a solid background in analysis and/or numerics of partial differential equations.

Lecture series

• Assoc. Prof. PhD Lukas Einkemmer (University of Innsbruck, Austria) • Low-rank approximation for nonlinear kinetic problems
  Due to the curse of dimensionality, solving high-dimensional partial differential equations numerically is extremely challenging. Complexity reduction techniques can alleviate the corresponding computational cost, but most classic methods assume a sufficiently regular solution. For hyperbolic equations this is often not a valid assumption. A promising approach to address such problems are so-called dynamical low-rank approximations. In this summer school we will provide an introduction to and discuss recent advances in constructing, analyzing, and implementing dynamical low-rank algorithms. In particular, we focus on applications to kinetic equations, which are widely used in plasma physics (e.g. in the study of Alfven waves).
• Asst. Prof. Dr. Anna Geyer (TU Delft, Netherlands) • Stability of nonlinear waves
  Determining the stability of solutions is of central importance when analyzing partial differential equations arising in applications, as it is typically the stable solutions that are observed in practise. This analysis is particularly challenging when the models are nonlinear, and often relies on the presence of symmetries and corresponding conservation laws, which are a common phenomenon in physical models. In this course we give an introduction to stability theory for nonlinear Hamiltonian equations. We will draw inspiration from linearisation and energy methods for stability theory in finite-dimensional dynamical systems (ODEs) and show how these concepts can be adapted to the infinite-dimensional setting (PDEs). We will apply the theory to several equations modeling wave propagation.

Schedule

From September 27-30, 2021. Have a look into the schedule. A more detailed program will follow later. Both speakers will give a lecture series accompanied by mini projects (with different focuses) for working in small groups. Additionally, there will be a poster session for PhD students and postdocs.

Registration

Registration has been closed. There is no fee. Please apply early, due to limited number of participants, until July 18th, 2021, by completing this email form and sending it to us. (Do you have trouble opening the link? Then copy & paste the email body manually and send it completed to admin∂waves.kit.edu.) Female PhD and Master's students are particularly encouraged to attend.

Venue

Karlsruhe Institute of Technology
Campus South, Building 20.30
Englerstr. 2
76131 Karlsruhe

Further directions.

Contact

Laurette Lauffer and Christian Knieling via E-Mail: admin∂waves.kit.edu

Local organizers

Marlis Hochbruck, Christian Knieling, Laurette Lauffer, Wolfgang Reichel