# Section for Mathematics

This section carries out fundamental mathematics research. We form the mathematical knowledge base for emerging new areas in the technical sciences, and we investigate new applications of pure mathematics.

This section carries out fundamental mathematics research. We form the mathematical knowledge base for emerging new areas in the technical sciences, and we investigate new applications of pure mathematics.

Algebra describes the underlying structure of mathematical objects as prime numbers, polynomials, symmetries, vector spaces, and on the lighter side also games, puzzles and even origami. It is therefore not surprising that there is a strong interplay between algebra and applications, especially applications involving discrete mathematics. An important example of this interplay studied by the algebra group is the theory of algebraic curves. Such curves can be used in information theory to construct excellent error-correcting codes for use in data communication, as well as locally recoverable codes that are used for distributed data storage in the cloud. Similarly, higher dimensional algebraic varieties are also used in information theory, notably for the construction of maximum rank-distance codes used in fast data transmission in computer networks.

Peter Beelen Professor

Maria Montanucci Associate Professor

Functional analysis is a branch of mathematical analysis, dealing with infinite-dimensional vector spaces and its operators. Functional analysis is a research topic by itself, but it is also a toolbox that provides insight into the underlying mathematical structure of problems in dynamical systems, geometry, optimization and other areas of applied mathematics. The Functional analysis group focuses on applications within harmonic analysis, where a key issue is how to decompose complicated signals in terms of elementary building blocks. The work in the group deals with the abstract theory of frames and its concrete manifestations in terms of structured frames in function spaces.

Ole Christensen Professor

Jakob Lemvig Associate Professor

Marzieh Hasannasabjaldehbakhani Assistant Professor (tenure track)

The geometry group develops novel theories, concepts, and applications related to the construction, analysis, and optimization of shapes in the most general sense of this very broad category, but also in its low dimensional concrete ramifications and approximations.

The research strategy of the group is focused on this - two-way - bridge between the general and the concrete.

Steen Schyum Markvorsen Professor

Jens Karl Gravesen Associate Professor

David Brander Associate Professor

A dynamical system is a system that changes over time in accordance with certain rules. Dynamical systems are central to both mathematics, science, and engineering. In the Dynamical Systems Group we study differential equations, as well as difference equations, from a dynamical systems point of view. We develop new theory and new methods, primarily around singular perturbation/slow-fast theory and the theory of complex dynamics. We also apply dynamical system theory to a range of problems in science and engineering, including fluid dynamics, chemistry, ecology, and mechanics.

Morten Brøns Professor, Head of section

Christian Henriksen Associate Professor

Kristian Uldall Kristiansen Associate Professor