Mathematics
Discrete Mathematics and Analysis & Differential Geometry
Discrete Mathematics investigates combinatorial objects that are discrete by nature (absence of continuity), such as graphs, set systems, or sequences. The group in Discrete Mathematics at IMADA works mainly on graphs and their relatives, which are omnipresent models for networks in science and technology. Whereas, at an introductory level, graph theory could be considered as part of a general mathematics or computer science education, the interaction of many fundamental invariants such as chromatic number and Hadwiger number is far from being well understood and subject of ongoing research in our group.
Modern analysis and differential geometry are two core subjects in mathematics. In our work we rely to a large extent on algebraic methods, such as homological algebra, Lie theory and K-theory. Our interests span from systems of linear transformations on Hilbert spaces, their symmetries and time evolutions, to integrable systems of partial differential equations and their geometrical interpretation. Many of the theories and problems that we work with stem from problems in physics, both classical and quantum, for instance gauge theory and quantum field theory.
People
| Jørgen Bang-Jensen | Professor | jbj @ imada.sdu.dk |
| Matthias Kriesell | Associate Professor | krisell @ imada.sdu.dk |
| Martin Svensson | Associate Professor | svensson @ cp3.sdu.dk |
| Wojciech Szymanski | Associate Professor | szymanski @ imada.sdu.dk |
| Bjarne Toft | Associate Professor | btoft @ imada.sdu.dk |
Group Leader
Bachelor Courses
Algebra, calculus, complex analysis, Hilbert and Banach spaces, measure theory, topology, differential geometry.
Graduate Courses and Independent Studies
Combinatorics and algebraic combinatorics, algorithmic complexity, combinatorial optimization, graph theory, matroids, operator algebras, symbolic dynamical systems, Riemannian and complex geometry, Lie theory, representation theory, Hodge theory, integrable systems.
Bachelor Projects
Algorithmic complexity, the Banach-Tarski-paradox, Cuntz algebras, graph algorithms, matroid theory, hypergraphs and other graph like concepts, invariant measures, visualisation of algorithms and concepts, minimal surfaces and surfaces of constant mean curvature, harmonic maps and calculus of variations, Clifford algebras and spinors.
Master Projects
Applications of graphs in social sciences and biology, C*-algebras and dynamical systems, digraphs and orientations, from graphs to matroids and back, graph C*-algebras, graph connectivity theory, graph minors, graph colorings, Hadwiger’s conjecture, Seiberg-Witten theory, infinite-dimensional Grassmannians, harmonic morphisms, quantum cohomology.