Profile
Profile

Prof. Dr. Herbert Koch

E-Mail: koch(at)math.uni-bonn.de
Telefon: +49 228 73 3787
Fax: +49 228 737658
Homepage: http://www.math.uni-bonn.de/people/koch/
Raum: 2.011
Standort: Mathematics Center
Institute: Mathematical Institute
Forschungsbereich: Research Area C4

Academic Career

1990

PhD, University of Heidelberg

1988 - 1992

Postdoc, University of Heidelberg

1992 - 1994

Visiting Assistant Professor, Northwestern University, Evanston, IL, USA

1994 - 2000

Postdoc, University of Heidelberg

2000

Habilitation

2000 - 2006

Professor (C4), University of Dortmund

2005 - 2006

Visiting Miller Professor, Mathematical Sciences Research Institute (MSRI), University of California, Berkeley, CA, USA

Since 2006

Professor (W3), University of Bonn

Research Profile

Partial differential equations provide a ‘language’ for describing phenomena ranging from geometry and analysis, physics and chemistry to engineering and economy. Central themes are the study of local properties of solutions and the passage from local considerations to global conclusions. The local regularity considerations of [3] imply regularity of solutions to the porous medium equation for large time without nondegeneracy conditions on the initial data. Carleman inequalities provide a robust alternative to monotonicity formulas. They provide an essential tool for the study of thin obstacles in the variable coefficient case [5]. Global existence and scattering for dispersive equations and the construction of conserved energies for the Korteweg-de Vries and the cubic nonlinear Schrödinger equation [1] are about global consequences of local properties. The self-similar solution to the generalized KdV equations [6] describe the structure of the blow-up.

The local analysis of three phase problems with triple lines of codimension 2 is challenging but it became accessible for the simplest model problems like thin obstacles. A first step consists in the proper linearization, and its connection to Calderón-Zygmund estimates. The quest for a more global understanding of dispersive waves is the driving motivation for many recent questions: Soliton resolution is a vague imprecise conjecture which I want to attack for the Korteweg-de Vries equation with PDE techniques. The Korteweg-de Vries equation is an asymptotic equation for water waves with finite depth. Global existence for small data may be within reach, with a study of the dynamics of the Gross-Pitaeviskii being an intermediate step.

Research Projects and Activities

DFG Collaborative Research Center SFB 611 “Singular Phenomena and Scaling in Mathematical Models”
Project leader, 2007 - 2012

DFG Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”
Project leader, since 2013

Publication List

MathSciNet Publication List (external link)

ArXiv Preprint List (external link)

Editorships

• Mathematische Annalen (2006 - 2014)
• Analysis and PDE (since 2008)
• SIAM Journal Mathematical Analysis (since 2012)

Awards

2005

Miller professorship, Miller Institute, Berkeley, CA, USA

Selected Invited Lectures

2004

International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, Madrid, Spain

2005

Analyse des Equations aux Dérivées Partielles, Forges-Les-Eaux, France

2017

DiPerna Lecture Berkeley, CA, USA

Habilitations

Flavius Guias (2006), now Professor, Fachhochschule Dortmund (University of Applied Sciences and Arts)

Axel Grünrock (2011), now apl. Professor, University of Düsseldorf

Selected PhD students

Adina Guias (2005): “Eine analytische Methode zur Punktereduktion und Flächenrekonstruktion”,
now Teacher, Phoenix Gymnasium

Sebastian Herr (2006): “Well-Posedness Results for Nonlinear Dispersive Equations with Derivative Nonlinearities”,
now Professor, University of Bielefeld

Martin Hadac (2007): “On the Local Well-Posedness of the Kadomtsev-Petviashvili II Equation”,
now in Consulting

Tobias Schottdorf (2013): “Global Existence without decay”,
now working at Cockroach Labs

Clemens Kienzler (2013): “Flat fronts and stability for the porous medium equation”,
now working at McKinsey

Dominik John (2013): “Uniqueness and Stability near Stationary Solutions for the Thin-Film Equation in Multiple Space Dimensions with Small Initial Lipschitz Perturbations”,
now in Consulting

Stefan Steinerberger (2013): “Geometric structures arising from partial differential equations”,
now Assistant Professor, Yale University, CT, USA

Angkana Rüland (2014): “On some rigidity properties in PDEs”,
now leader of Max Planck Research Group at the Max Planck Institute for Mathematics in the Sciences, Leipzig

Habiba Kalantarova (2015): “Local Smoothing and Well-Posedness Results for KP-II Type Equations”,
now Associate Professor, Baku, Azerbaijan

Christian Zillinger (2015): “Linear Inviscid Damping for Monotone Shear Flows, Boundary Effects and Sharp Sobolev Regularity”,
now Postdoc, University of Southern California, Los Angeles, USA

Supervised Theses

  • Master theses currently: 2
  • Diplom theses: 4, currently 2
  • PhD theses: 10, currently 7
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