Research
Mathematics Computer Science Mathematical and Computational Life Sciences Data Science
Bridging the gap between computer science, mathematics, and other research fields forms the core of my research. A specific emphasis lies on discrete mathematics and theoretical computer science, which are crucial for comprehending the intricacies of complex problems and devising efficient solutions. In addition, my research focuses on the mathematical characterization of discrete data and the development of mathematical theory to help understanding the complex processes in life sciences. Grasping the structure of the underlying problems is crucial for answering fundamental questions: How do we best extract knowledge out of the given data and how can we do it efficiently? Answering these questions is an important step towards concrete, practical and innovative algorithms and applications.
From a theoretical point of view, my work includes- Discrete Mathematics (incl. Graph Theory, Discrete Optimization, Combinatorics)
- Computational Complexity (incl. (Co)NP-completeness, Fixed-Parameter Tractability (FPT))
- Design of Integer Linear Programs (ILPs) and techniques to solve them.
- Design of efficient exact algorithms and efficient heuristics
- Design of approximation algorithms with provable guarantees on the distance to the optimal solution
- Matroid Theory
- Embeddings of combinatorial objects into orientable manifolds
- Network-based analysis of experimental data
- Statistical analysis and learning from data
- Understanding the mathematics of and design of efficient editing heuristics for (Reciprocal) Best Matches (as e.g. inferred with BLAST)
- Understanding the mathematics of and design of efficient algorithms for the automated inference of Horizontal Gene Transfer
- Phylogenomics, Orthology detection and inference, Rare genomic events
- Self-assembling Nano structure (Proteins, RNA) and Atom Tracking in Chemical Reaction Networks
- Combinatorial RNA secondary structures
- Gene/PPI interaction networks
- Sonification of Sequence Alignments