A5087139366- Advanced Operator Algebra Research
- Homotopy and Cohomology in Algebraic Topology
- Geometry and complex manifolds
- Geometric and Algebraic Topology
- Geometric Analysis and Curvature Flows
- Advanced Topics in Algebra
- Advanced Algebra and Geometry
- Atomic and Molecular Physics
- Laser-induced spectroscopy and plasma
- Advanced Differential Geometry Research
- Holomorphic and Operator Theory
- Laser-Plasma Interactions and Diagnostics
- History and Theory of Mathematics
- Laser Design and Applications
- Laser-Matter Interactions and Applications
- Nuclear physics research studies
- Algebraic Geometry and Number Theory
- Advanced Differential Equations and Dynamical Systems
- Ophthalmology and Eye Disorders
- Surface Roughness and Optical Measurements
- Black Holes and Theoretical Physics
- Economic and Social Issues
- Crystallization and Solubility Studies
- Elasticity and Material Modeling
- Mathematical and Theoretical Analysis
University of Freiburg
2007-2025
Ollscoil na Gaillimhe – University of Galway
2020
Bielefeld University
2016
Asklepios Klinikum Harburg
2016
Springer Nature (Germany)
2016
Technische Universität Berlin
2016
Weierstrass Institute for Applied Analysis and Stochastics
2016
GSI Helmholtz Centre for Heavy Ion Research
2005-2013
Ludwig-Maximilians-Universität München
2007
Johns Hopkins University
2004
At the Helmholtz center GSI, PHELIX (Petawatt High Energy Laser for heavy Ion eXperiments) has been commissioned operation in stand-alone mode and, combination with ions accelerated up to an energy of 13 MeV/u by ion accelerator UNILAC. The heavy-ion beams available at GSI enables a large variety unique experiments. Novel research opportunities are spanning from study ion–matter interaction, through challenging new experiments atomic physics, nuclear and astrophysics, into field relativistic...
This paper reports on the status of PHELIX petawatt laser which is built at Gesellschaft fuer Schwerionenforschung (GSI) in close collaboration with Lawrence Livermore National Laboratory (LLNL), and Commissariat à l'Energie Atomique (CEA) France. First experiments carried out chirped pulse amplification (CPA) front-end will also be briefly reviewed.
In this article, a six-parameter family of highly connected 7-manifolds which admit an $\mathrm{SO}(3)$-invariant metric non-negative sectional curvature is constructed and the Eells-Kuiper invariant each computed. particular, it follows that all exotic spheres in dimension 7 curvature.
The purpose of this paper is to give an explicit local formula for the difference two natural versions equivariant analytic torsion in de Rham theory.This sum integral a Chern-Simons current and new invariant, V -invariant odd dimensional manifold equipped with action compact Lie group.The localizes on critical manifolds invariant Morse-Bott functions.The results are shown be compatible Bunke, also our previous forms.
We extend the adiabatic limit formula for \eta -invariants by Bismut–Cheeger and Dai to Seifert fibrations. Our contains a new contribution from singular fibres that takes form of generalised Dedekind sum. As an application, we compute Eells–Kuiper t-invariants certain cohomogeneity one manifolds were studied Dearricott, Grove, Verdiani, Wilking, Ziller. In particular, determine diffeomorphism type manifold positive sectional curvature.
We present a formula for the full Cheeger-Chern-Simons class of tautological flat complex vector bundle rank 2 over BSL(2, C δ ).Our improves in [DZ], where is only computed modulo 2-torsion.
We give an overview over the higher torsion invariants of Bismut-Lott, Igusa-Klein and Dwyer-Weiss-Williams, including some more or less recent developments.
We generalise the Kreck-Stolz invariants <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="s 2"> <mml:semantics> <mml:msub> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:annotation encoding="application/x-tex">s_2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and 3"> <mml:mn>3</mml:mn> encoding="application/x-tex">s_3</mml:annotation> by defining a new invariant, alttext="t"> <mml:mi>t</mml:mi>...
Let p: M -> B be a family of compact manifolds equipped with unitarily flat vector bundle F M. We generalize Igusa's higher Franz-Reidemeister torsion τ(M/B;F) to the case that fibre-wise cohomology H^*(M/B;F) carries parallel metric. If moreover admits Morse function, we compute difference and analytic \Cal T(M/B;F). also generalise examples given in math.DG/0111222 .
We compute the Eells-Kuiper invariant of Berger manifold SO (5)/SO (3) and determine that it is diffeomorphic to total space an S 3 -bundle over 4 . This answers a question raised by K. Grove W. Ziller.
We derive a formula for the η-invariants of equivariant Dirac operators on quotients compact Lie groups, and their infinitesimally extensions.As an example, we give some computations spheres.
In this article, a six-parameter family of highly connected 7-manifolds which admit an SO(3)-invariant metric non-negative sectional curvature is constructed and the Eells-Kuiper invariant each computed. particular, it follows that all exotic spheres in dimension 7 curvature.
We compute explicitly, and without any extra regularity assumptions, the large time limit of fibrewise heat operator for Bismut–Lott type superconnections in L^2 -setting. This is motivated by index theory on certain non-compact spaces (families manifolds with cocompact group action) where convergence at implies refined -index formulas. As applications, we prove a local theorem families signature operators an -Bismut–Lott theorem, expressing Becker–Gottlieb transfer flat bundles terms...
We generalize Llarullâs scalar curvature comparison to Riemannian manifolds admitting metric connections with parallel and alternating torsion having a nonnegative operator on $\Lambda ^2TM$. As by-product, we show that the Euler number signature of such are determined by their global holonomy representation. Our result holds in particular for all quotients compact Lie groups equal rank, equipped normal homogeneous metric. also correct mistake treatment odd-dimensional spaces our earlier papers.
In this note, we consider the Dirac operator $D$ on a Riemannian symmetric space $M$ of noncompact type. Using representation theory, show that has point spectrum iff ${\hat A}$-genus its compact dual does not vanish. case, if is irreducible, then $M=\mathrm {U}(p,q)/\mathrm {U}(p)\times \mathrm {U}(q)$ with $p+q$ odd, and $\operatorname {Spec}_{p}(D)=\{0\}$.
When two smooth manifold bundles over the same base are fiberwise tangentially homeomorphic, difference is measured by a homology class in total space of bundle. We call this relative structure class. Rationally and stably, complete invariant. give more or less self-contained exposition theory. An important application computation Igusa-Klein higher Reidemeister torsion invariants these exotic structures. Namely, invariant equal to Poincaré dual image base. This proved companion paper...
We compare the higher analytic torsion of Bismut and Lott a fibre bundle p: M -> B equipped with flat vector F fibre-wise Morse function h on T that is constructed in terms families Thom-Smale complex associated to F, thereby extending previous joint work Bismut. Under additional conditions related Igusa's Franz-Reidemeister torsion. As an application, we use detect infinite smooth bundles p_i: diffeomorphic fibres are homeomorphic but not as bundles.