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Henrik Ueberschär
Institut de Mathématiques de Jussieu
BC 247
CNRS U. M. R. 7586
Campus Pierre et Marie Curie
Sorbonne Université
75005 Paris
France
Email: henrik dot ueberschar at imj-prg dot fr
About myself:
I am an associate professor (maître de conférences HDR) and a member of the Functional Analysis group here at Jussieu. I previously conducted postdoctoral research at Université de Lille, MPIM Bonn, CEA Saclay and Tel Aviv University. I obtained my PhD from the School of Mathematics, University of Bristol, under the supervision of Jens Marklof.
My research is concerned with Quantum Chaos and Disordered Systems. We study how the underlying classical dynamics manifests itself in the geometric and statistical properties of the wave functions and energy levels of a quantum system. I am particularly interested in quantum systems in a state of transition - so-called intermediate systems. Examples are pseudointegrable billiards or disordered systems near the Anderson transition. The wave functions of intermediate systems often display a self-similar structure at a multitude of scales - a phenomenon known as "Quantum Multifractality". I am interested in a rigorous mathematical proof of multifractal scaling laws for the wave functions of such systems.
Research interests:
Quantum Chaos
Spectral Theory and Spectral Geometry of (random) Schrödinger operators
Semiclassical Analysis
Quantum Multifractality