Bioinformatics, computational genomics and modeling molecular evolution
Together with my students I work on theoretical aspects of modeling molecular evolution as well as data-driven applications of our new methodologies. We are broadly interested in applying computational methods to study the process of gene and genome evolution and in particular the process of adaptive genetic change. Growing genome-scale sequences and information from complimentary disciplines of transcriptomics, proteomics and metabolomics have begun to seriously impact genomics. But the challenge of understanding the dynamics of such large-system data can only be met through an integration of organism, molecular, and mathematical disciplines. New techniques need to be developed for discovering complex patterns from multi-faced systems biology data.
Network simulation and graph mining
Multicriteria Parameter Optimization in scientific and technical applications
Metamodelling (Response Surfaces)
Sensitivity and robustness studies for high resolution simulation results
Correlation analysis for high resolution simulation results
Hierarchical linear solvers, in particular, algebraic multigrid methods
Applied mathematics: approximation theory and applied harmonic analysis.
Harmonic analysis: Wavelet analysis, complex wavelets, phase information, complex splines
Integral transforms for signal and image analysis
Applications in signal and imaging processing
Approximation theory, sampling and interpolation
Function theory: Nonharmonic Fourier and Dirichlet series, growth estimates for entire functions of special type
Numerical methods for time-dependent partial differential equations
Iterative methods for solving large linear systems of equations and eigenvalue problems
Approximation of matrix functions
Applied harmonic analysis and geometric multiscale analysis, in particular time–frequency analysis, wavelet theory and shearlet theory
Approximation theory, in particular sparse approximation and compressed sensing
Frame theory, in particular theory of redundant systems
Mathematic data analysis, in particular signal processing and image processing
Mathematical Data Science
My research area is in the field of mathematical optimisation. The (further) development of effective algorithms for both NP-hard problems and polynomial solvable problems is of particular interest to me. It is my aim to develop practically efficient but, above all, exact algorithms, to implement them in terms of algorithm engineering and to evaluate them for use in relevant applications. I enjoy studying problems that have applications in the natural sciences, for instance in physics, but also in operations research. My work focuses on combinatorial optimisation, polyhedral combinatorics and graph algorithms.
An additional focus of my research is the further development of general methods in nonlinear optimisation, for example in binary constrained quadratic optimisation.
I am the head of a young researcher group in the Department of Computer Science at the University of Cologne within the framework of the German Research Foundation Emmy Noether Programme. The research topic for this project is the development of exact optimisation algorithms for problems in theoretical physics. Frequently, these algorithms can be applied to solving problems in other fields.
Stochastic modelling and simulation. Computational Biology. Numerical Analysis. Synthetic Biology.
Multiscaled and hybrid methods, spatio-temporal stochastic simulation algorithms for chemical kinetics
Simulation of cell processes including permeability, delays, anomalous diffusion and directed transport
Synthetic Biology / Bioengineering
Modelling of neural cells and circuits, focusing on unraveling the role of dendrites and dendritic computations in learning and memory.
Development of computational methods and tools for bioinformatics analysis of biological data, focusing on miRNAs and cancer diagnostics.
Systems biology approaches for understanding neural and gene functions.
History of mathematics in the 16th and 19th/20th centuries
History of astronomy from the 16th to the 19th centuries
Current area of research:
Gauss and Russia, a ca. 800-page comprehensive work written with Dr Elena Roussanova
Nonlinear and partial differential equations
Well-posedness of problems arising from phase transition-separation phenomena
Memory effects in phase transitions phoenomena
Long time behaviour and existence of the attractor for nonlinear/singular phase-field systems
Inverse problems: identification of memory kernels in PDE systems
Max-Planck-Institut für Dynamik und Selbstorganisation (MPIDS), Göttingen
The nature of turbulent flows, in particular, physics of turbulent thermal convection. This includes investigation of natural, forced and mixed convection; coherent flow structures, boundary layer structures, small-scale turbulence in buoyancy-driven flows; the influence of rotation, non-Boussinesq effects, non-monotone fluid properties, wall roughness and domain geometry on turbulent convection. Apart from physics of turbulence itself, the research interests include also all numerical issues and aspects of turbulence simulations. Research interests in natural and applied sciences and engineering include in particular the large-scale oceanic circulation, wind chill effects in hot and cold regions, supergranulation in the solar upper convective zone, heat and mass transfer in nanofluids, surface-tension-driven convection and vibration-induced convection in low gravity, improvement of the efficiency of technological heating and cooling processes, control of ventilation processes in living quarters and in transport.
My research interests include all aspects of string theory, gravitational physics and quantum field theory. In recent years much of my work has been focused on holographic dualities and their implications. Holography relates gravitational theories to theories without gravity in one less dimension and represents a completely new understanding of both gravity and the dual non-gravitational theories. My work on holography encompasses both foundational issues (the holographic dictionary between gravity and gauge theory physics) and applications of holography to black hole physics, phenomenology and condensed matter systems.
Income distribution, inequality, poverty
Extreme value modeling, copulas (for applications in finance)
Generalised linear models, latent variable models (for applications in psychology)
Time series modeling, wavelet decomposition (for applications in engineering)
Model selection with large datasets (for applications in economics and genetics)
Computational and mathematical approaches to music research
Music information retrieval
Mathematical music theory
Computational music analysis
Oral transmission in folksongs
Musical performance research
Rhythm and meter in music
My research focuses on the dynamics of granular materials, with a special interest in geophysical phenomena occurring in nature and engineering problems in industry. Granular materials span a range of scales, from the micro-scale in grain phenomena to the macro-scale in large systems such as avalanches and dunes. Despite their importance, granular materials remain poorly understood; due to the lack of a comprehensive physical description, mathematical tools and techniques are insufficient to fully predict behavior of granular materials in industrial and natural applications at this time.
In my research program I aim to gain a deeper understanding of the physics of granular materials across all different scales and flow regimes. My interests can be classified into the following areas:
1) wave propagation in a particulate material
2) avalanching of a granular material and
3) near-surface geophysical techniques to characterize soil, sand and geophysical mass flows.
Although I am first and foremost an experimentalist, I also employ numerical simulations to develop analytical models and to form a comprehensive picture of open research questions.
As a statistician, I work with biological datasets to understand the mechanisms underlying human disease and identify possible treatments. Such work is only possible with close collaboration with biologists, and I moved to the Cambridge Institute for Medical Research in 2009 to pursue these collaborations. During the GWAS era, we, and others, identified many genetic polymorphisms that alter risk of human diseases such as type 1 diabetes and hypertension. My focus has now mostly shifted towards identifying the molecular function through the pleiotropic effects of these variants on disease and intermediate biological traits such as gene expression. Statistically, my current work is focused on variable selection, Bayesian model averaging, and methods to integrate data from GWAS scans of related traits.
Geometry and topology
Deformation spaces of geometric structures on manifolds
Representation varieties of surface groups
Higher Teichmueller spaces
Discrete subgroups of Lie groups