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Research
I am deputy speaker of CRC 1173 "wave phenomena -- analysis and numerics" and I am involved with the following projects:
- A6 Time-periodic solutions for nonlinear Maxwell equations
- A10 Standing and moving pulses in periodic media
- B3 Frequency combs
I am speaker of the area of methods "Mathematical modeling, differential equations, numerics, simulation" of the KIT-Center MathSEE "Mathematics in Sciences, Engineering, and Economics".
Vorträge (Auswahl)
9. Juni 2021, INdAM Workshop Nonlinear Phenomena: between ODEs and PDEs, Rome
Time-periodic solutions of semilinear wave equations
20. September 2018, 6th GAMM Workshop on Analysis of PDEs, Stuttgart
Real-valued time-periodic localized standing waves for a class of nonlinear wave equations
17. Mai 2017, WAVES, Minneapolis
Localized time-periodic solutions of nonlinear wave equations
22. Mai 2017, International Conference on Elliptic and Parabolic Problems, Gaeta
Localized time-periodic solutions of nonlinear wave equations
2. Dezember 2016, Recent progress in PDEs, Marseille
Localized time-periodic solutions of nonlinear wave equations
23. Juni 2016, PDEs at the Grand Paradis, Cogne, Italy
A variational approach to real-valued breathers for a class of cubic nonlinear wave equations
14. September 2015, VII Symposium on Nonlinear Analysis, Torun, Poland
Standing waves for nonlinear curl-curl wave equations
9. Juli 2014, AIMS Madrid
Ground states of a nonlinear curl-curl problem
7. November 2011, Workshop on Nonlinear Differential Equations, Pienza
The Paneitz equation in hyperbolic space
28. Juni 2010, Graduiertenkolleg-Seminar
Surface Gap Solitons
Meine Arbeitsgruppe
Die Arbeitsgruppe besteht neben mir aus
Doktoranden (aktuell)
- MSc. Florian Babisch (seit 11/2025)
- MSc. Julia Henninger (seit 10/2021)
PostDocs (aktuell)
- Laura Baldelli, PhD (seit 10/2025)
Abgeschlossene Promotionen
- Dr. Lukas Bengel (Promotion 15.10.2025)
Dr. Sebastian Ohrem (Promotion 23.7.2025) - Dr. Elias Gasmi (Promotion 16.11.2022)
- Dr. Simon Kohler (Promotion 23.06.2021)
Variational techniques for breathers in nonlinear wave equations
- Dr. Janina Gärtner (Promotion 20.02.2019)
Continuation and Bifurcation of Frequency Combs Modeled by the Lugiato-Lefever Equation
- Dr. Carlos Hauser (Promotion 20.02.2019)
- Dr. Piotr Idzik (Promotion 20.09.2017)
- Dr. Andreas Hirsch (Promotion 07.06.2017)
Mono- and polychromatic ground states for semilinear curl-curl wave equations
- Dr. Anton Verbitsky (Promotion 25.06.2014)
- Dr. Hans-Jürgen Freisinger (Promotion 26.06.2013)
Grenzflächenprobleme bei der nichtlinearen Schrödingergleichung
- Dr. Rainer Mandel (Promotion 23.01.2013)
Grundzustände, Verzweigungen und singuläre Lösungen nichtlinearer Schrödingersysteme
In the Karlsruhe PDE seminar external experts present results from analysis and numerics of partial differential equations. The seminar takes place about three times per semester as a special version of the CRC seminar. Since summer term 2016, the canonical time and location of the PDE seminar is
Thursday, 2:00-3:00 p.m., in SR 1.067 in the Math building 20.30.
Nonlinear PDE Days
Frankfurt - Giessen - Karlsruhe - Köln
Previous PDE days
August 22-23, 2018 at Frankfurt
Local and Nonlocal Problems in Geometry and Mathematical Physics
October 13-14, 2016 at Giessen
Junior Nonlinear PDE Days
July 14-15, 2015 at KIT
Nonlinear PDE Days
June 12-13, 2014 at Cologne
PDE Days
July 4-5, 2013 at Giessen
Workshop on Geometric PDEs
March 6-7, 2013 at Frankfurt
Nonlinear Evolution Equations
July 17-18, 2012 at KIT
Variational Methods in Mathematical Physics
October 4-5, 2011 at Cologne
Nonlinear PDE days in Köln
June 16-17, 2011 at Giessen
Concentration phenomena in nonlinear PDE's
January 20-21, 2011 at KIT
Computational aspects and computer-assisted proofs in nonlinear PDEs
July 1-2, 2010 at Frankfurt
Analytical and computational methods in geometric optimization problems
January 21-22, 2010 at Giessen
Liouville theorems and applications
June 25-26, 2009 at Karlsruhe
Nonlinear Schrödinger Equations
DMMM winter school ”Mathematics for Engineering Applications”
Slides of January 27,2020 -- 1. Update, Fehler behoben
Notes on bifurcation theory
CIME Sommerschool 2017
Geometry of PDE's and related problems
The contributions to this summer school were published.
AIMS Springschool 2015
Lecture notes: final version 4 of February 27th, 2015.
ACAMiMM Sommerschule 2013 für Studierende
Erasmus Lifelong Learning Program: Intensive Program
1.-15. September in HAJDUSZOBOSZLO/Ungarn: ACAMiMM
ACAMiMM Sommerschule 2011 und 2012 für Studierende
In 2011 the summer school took place in Bydgoszcz/Polen from September 4-18.
In 2012 the summer school took place in Freudenstadt from September 9-23.
At the summer school in Bydgoszcz, Professor Roman Ger spoke about convexity as follows:
"Convexity is a beautiful lady -- and I am a silent admirer of her".
In full accordance with his statement, I drew the following sketch on the black board at the beginning of my lecture series on "Calculus of Variations and Applications to Elasticity":
"Convexity is truly a beautiful lady -- but do you also know her beautiful sisters?"
It found its way into Macierzator 40 published by the mathematics students at the Silesian University in Katowice, whom I cordially thank for that.