Research

Dynamics and Uncertainty

In broad strokes, research at the department of Mathematics can be summarized
as follows. On the one hand we are active on a fundamental and theoretical
level; on the other hand we also work in an applied and practical environment
with links to many sciences and societal issues. Much of our research effort
can be captured with the phrase "Dynamics and Uncertainty", two of the main
characteristics of mathematics at large. "Dynamics" relates to the
understanding and description of everything that changes, while
"Uncertainty" relates to those situations in which we have only partial
information, for whatever reason. Obviously these concepts have strong
interactions, and they can be approached both on a fundamental and an applied
level.

We present here our research in seven overlapping themes. In most themes,
dynamics and uncertainty both play a role. Furthermore, almost all themes have
fundamental and applied aspects, indicating the strong and important links
between mathematical research and the world we live in. Mathematics is of
course about proving theorems, but we are very much aware of the fact that
mathematics has always been inspired by the world outside, and, the other way
around, that our society greatly benefits from mathematics as well. It is this
two-way inspiration that we seek to pursue.
 

 

Biomathematics

biostatistics, statistics for life sciences, mathematical biology, statistical genetics, brain imaging, statistics for neuroscience, population dynamics, systems biology

Business Analytics

E-health, optimization of business processes, operations research, call centers, queuing theory, health care logistics, statistics

Determinism and Randomness

probability theory, stochastics, dynamical systems, stochastic differential equations, random processes, statistical physics

Geometric Dynamics

symplectic geometry, symmetries in dynamical systems, variational methods, spatial probability, percolation, Morse-Conley-Floer theory

Modelling and Statistics

statistical models, partial differential equations, mathematical physics, financial mathematics, control theory, industrial mathematics

Patterns in Complex Systems

statistics of high-dimensional data (neuro-imaging, microarrays), datamining, large systems of nonlinear differential equations, dynamics in biological networks

Shape and Structure

Algebraic K-theory, number theory, arithmetic algebraic geometry, homotopy theory, symplectic topology, toric topology, infinite-dimensional topology, dimension theory, convex geometry.