Discrete Mathematics
Our research group focuses on structural and extremal combinatorics, discrete algorithms and combinatorial limits. We advance these areas by applying techniques from analysis, logic and probability, often employing computational approaches. We also develop and apply mathematical methods to address problems of interest in computer science, with a particular focus on algorithm design.
Research
We work on a broad range of problems in graph theory, which is arguably the area of mathematics with most applications in computer science. We are primarily interested in problems concerning the interplay between chromatic and structural properties of graphs and structural characteristics of graph classes (defined e.g. by forbidden substructures or recursively). The latter relates to the study of width parameters of graphs, matroids and other combinatorial structures, which play a central role in algorithm design, particularly, in parameterized complexity.
We also approach problems in extremal combinatorics using the methods of the theory of combinatorial limits, which forms a bridge from combinatorics to analysis, ergodic theory, group theory and probability theory. One line of our research revolves around quasirandomness and the extremality of (quasi)random constructions, which link to fundamental problems in extremal combinatorics such as Sidorenko's Conjecture as well as to application in data analysis and statistics.