Bernd Kirchheim is a plenary speaker and professor of mathematics at the Leipzig University, Germany.
Working with David Preiss, Bernd received his PhD from the Charles University Prague in 1999 and his habilitation in 2002 while at the Max Planck Institute for Mathematics in the Sciences Leipzig. After this he had been affiliated for nearly ten years with the University of Oxford, before returning in 2012 to Leipzig. He was awarded the Whitehead prize of the LMS and is mainly interested in Geometric measure theory and the (vectorial) Calculus of Variations.
Derivatives and their geometry
What is the range of the derivative of a (lipschitz) map, more precisely the possible distributions of it? This question was motivated by variational problems, where the direct method fails. The methods developed to answer this found many applications - from fluid dynamics to the study of surfaces.
We will discuss the underlying geometry in matrix space, where appropriate convexity notions give the crucial inside, and recent progress on homogeneous functionals. Some remaining geometrical question with impact on the regularity of surfaces will be presented.