Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation
maximize

Prof. Dr. Thomas Gerstner

E-Mail: gerstner.ins.uni-bonn.de
See also: http://www.math.uni-frankfurt.de/~gerstner/
URL: http://wissrech.ins.uni-bonn.de/people/gerstner.html

Former member of the institute

Now at Universitaet Frankfurt (http://www.math.uni-frankfurt.de/~gerstner/)

Research Interests:

Cluster of Excellence: Hausdorff Center for Mathematics
Project Area J: High-dimensional problems and multi-scale methods
Numerical Quadrature in Finance

Pricing of contingent claims, path- and performance-dependent options, Brownian bridge construction, principal component analysis, adaptive sparse grids, dimension reduction.

Sparse Grids

Numerical interpolation and integration on sparse grids, hierarchical tensor-product bases, combination technique, curse of dimensionality.

Meteorological Data Analysis

Weather radar measurements, meteorological visualization systems, volume rendering, data dependency modelling, neural networks.

Molecular Visualization

Fast multiresolution display of transparent isosurfaces, electron densities, visualization of bonds and atomic positions, data exploration.

Multiresolution Isosurface Extraction

Adaptive hierarchical tetrahedral meshes, recursive bisection, fast extraction algorithms, error indicators, topology preservation, controlled topology simplification.

Fractal Landscape Classification

Hierarchical fractals, computation of fractal exponents, fast inverse data fitting, artificial terrain generation.

Compression of Large-Scale Spatial Data

Efficient in-memory data compression, pointer-less representation of hierarchical data structures, space-filling curves, interactive visualization of global topographic data.

Hierarchical Terrain Representation

Digital elevation models, adaptive hierarchical triangulations, recursive bisection, wavelets on triangulations, constrained triangulations, preservation of topography.

Completed Research Projects

Cluster of Excellence: Hausdorff Center for Mathematics
Project Area H: Stochastic market models and aggregation
BMBF support program: Mathematik für Innovationen in Industrie und Dienstleistungen
FIDEUM: Modellierung und Bewertung von Finanzderivaten in unvollständigen Märkten
Cooperation with DZ Bank, Theta Engineering, TU München, Universität Heidelberg, Zürich Gruppe
REMO: Complex Retrieval and Monitoring Scenarios in Science and Engineering initiative of the University of Bonn
Trend Prediction of Exchange Rate with Regularization Networks on Dimension-Adaptive Sparse Grids
Medical Imaging

Interactive volume visualization, slicing, parallel isosurface extraction, handling of large MRI and CT data sets.

Progressive Image and Video Transmission

Tree and tree-front image coding, space-filling curves, hierarchical triangulations, quality of service, video conferencing.

ESF Program: Advanced Mathematical Methods for Finance (AMaMeF)
Adaptive numerical valuation methods for Bermudean options
ESF Program: Advanced Mathematical Methods for Finance (AMaMeF)
Sparse grid discretizations for jump diffusion processes
BMBF support program: Mathematik für Innovationen in Industrie und Dienstleistungen
Numerische Simulation für Asset/Liability Management im Versicherungswesen
Cooperation with Deutscher Herold, Zürich Gruppe
SFB 611: Singular phenomena and scaling in mathematical models
Project C2: Adaptive and robust multigrid methods for space time discretizations
SFB 611: Singular phenomena and scaling in mathematical models
Project C1: Wavelet Methods for Systems of Operator Equations

Finished Projects


Publications

Talks

Teaching