The Fall School door-oceanis jointly organized by AIMS Senegal and the Goethe-University Frankfurt, and it is funded by the DAAD
Germany within the project “Joint Steps in Geometric Variational Problems and Related Functional Inequalities”. In addition to participants from AIMS Senegal, up to 20 junior scientists are invited participate.

The scientific program and meals will take place at the African Institute for Mathematical Sciences (AIMS) in Mbour, Senegal, situated approximately eighty kilometers south of Dakar at the Atlantic Coast. Accomodation will be arranged by AIMS in a nearby hotel (nightly rate around 60 €). Transport from the Airport Dakar to the hotels will be arranged by AIMS as well.

Speakers:

  • Helmut Abels (Universität Regensburg)
  • Moritz Kaßmann (Universität Bielefeld)
  • Nicola Kistler (Goethe-Universität Frankfurt)

Organizers:

  • Mouhamed M. Fall (AIMS Senegal Mbour)
  • Tobias Weth (Universität Frankfurt)

The conference programm will include four minicourses given by the speakers listed above.

1. Helmut Abels:  Abstract evolution equations and applications 

Abstract: Many kinds of evolution equations (i.e., equations with a time like variable) can be considered as an abstract ordinary differential equation in a suitable Banach space. We will discuss how classical results from ODE theory like the Picard-Lindelöf Theorem or the principle of linearized stability can be carried over to similiar results for suitable abstract evolution equations. The results depend much on the strength of the nonlinearities . Several cases, which correspond to linear, semi-linear and quasi-linear differential equations, will be treated. Moreover, we will discuss several applications e.g. to equations from fluid mechanics, geometric evolution equations and free boundary value problems.

2. Moritz Kassmann: Regularity questions for integro-differential operators

Abstract: In this course, we will study integro-differential operators
that satisfy the maximum principle. We will carefully introduce them and
explain their probabilistic counterpart, Markov jump processes. We will
then use techniques from analysis and probability to prove some
regularity results for solutions to corresponding integro-differential
equations.

3. Nicola Kistler: The F-KPP equation, traveling waves and branching Brownian motion

Abstract: The Fisher, Kolmogorov-Petrovsky-Piscounov equation is arguably the simplest partial differential equation which admits traveling waves. The asymptotical speed of the standing wave has been first identified by Kolmogorov et. al in the 30’s, but the exact location of the front has been settled by Bramson only in the late 70’s. The tools employed by Kolmogorov et. al. were purely analytical, whereas Bramson exploited a representation of the solutions of the p.d.e. in terms of functionals of a stochastic particle system known as branching Brownian motion. Recently, this old problem at the boundary between analysis and probability has been vigorously taken up again, mostly due to unexpected links with other realms such as mathematical physics, and even number theory. Because of these developments, the field has become very vast: I will try to convey some of the main ideas.

In addition, a number of additional participants will be invited to give 20min talks. Every participant is offered the opportunity to present a poster.

To apply for participation, please send a short motivational letter and a CV (pdf files) to

habash@math.uni-frankfurt.de.

For participants from Germany, DAAD offers up to 11 grants to cover travel and accomodation expenses up to 1000 € (up to 775 € for travel expenses, up to 225 € for the hotel)  according to the DAAD regulations. Similarly, for other participants, a small number of grants are funded by the endowed chair in “Mathematics and its Applications” at AIMS, Senegal. Please let us know in your motivational letter in case you wish to apply for one of these grants. 

Please submit your application until

September 30, 2016.

Every applicant will be notified until October 10, 2016 whether he/she is invited to participate.

The spring school is supported by: