Permanent Faculty
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Christian Henriksen, Associate Professor
Keywords: Dynamical systems, Industrial Mathematics, Complex Analysis, Potential Theory, Holomorphic Dynamics
I'm broadly interested in mathematics and how to apply it to real world problems. On a more pure level, I'm interested in the dynamics of holomorphic mappings, such as those of extremal polynomials. The techniques I use, come from the theory of quasiconformal maps and deformations, holomorphic motions and potential analysis. read more
David Brander, Associate ProfessorKeywords: differential geometry, harmonic maps, nonlinear integrable PDEs, loop group methods, surface theory, applied differential geometry
I study classes of surfaces that are represented by integrable PDE, i.e., partial differential equations that admit a so-called "Lax pair" formulation. In particular surfaces associated with both Riemannian and Lorentzian harmonic maps into a symmetric space. I use the theory of loop groups to construct solutions both analytically and numerically. In applied geometry I work on applications of differential geometry to architectural design as we well as problems of shape recognition read more
Jakob Bohr, ProfessorKeywords: Differential geometry, topology, number theory, tilings, close packing, topological inequalities, Knot theory, framed space curves, framed knots, D-forms
Applications of differential geometry in problems where geometry provides a guiding principle in natural science. The structure of the nucleosome is one such example. A byproduct of the analysis is the geometrical reason behind the minimum number of base-pairs in a double stranded plasmid.From a point of view of mathematical applications is the detailed description of D-forms as being the convex hull of closed space curves and in this connection the renewed relevance of the four-vertex theorem and related theorems. read more
Jakob Lemvig, Associate ProfessorKeywords: frame theory, Fourier analysis, functional analysis, Gabor analysis, harmonic analysis, signal processing, shearlets, time-frequency analysis, wavelets
My main objective is advancing the understanding of data, signals, and functions occurring throughout engineering and mathematics using linear transforms. The key challenge is constructing and analyzing new transforms that reveal the desired information of the data/signals of interest. I work in the abstract setting of harmonic analysis and frame theory in Hilbert spaces as well as its many concrete manifestations, e.g., wavelet and time-frequency analysis of square-integrable functions. read more
Jens Gravesen, Associate ProfessorKeywords: Differential geometry, geometric design, isogeometric analysis, applications in quantum mechanics, applications in nano technonlogy
My research started in pure mathematics in the fields of differential geometry and global analysis. I have now moved in to more applied mathematics especially geometric design and isogeometric analysis. I am especially interested in representations of curves, surfaces, and other geometric objects that allows for exact calculations. Another part of my research is concerned with geometric effects in quantum mechanics, with a view to applications in nano technology. read more
Johan Rosenkilde, Associate ProfessorKeywords: discrete mathematics, algebra, computer algebra, error-correcting codes, coding theory, cryptography, number theory, finite fields, algebraic curves, algorithms, exact computation
I research in fast algorithms for exact computation in discrete algebra, with an emphasis on applications in digital communication, especially error-correcting codes and cryptography. These two serve opposite purposes in a sense: cryptography hides information from spying eyes, while error-correcting codes protects a message from errors that occur during storage or transmission. Central in all of this is efficient algebraic computation, such as solving special equations over finite fields or polynomials on the fly. I use algebraic curves and number theory as powerful tools for constructing good solutions. read more
Kristian Uldall Kristiansen, Associate ProfessorKeywords: dynamical systems, differential equations, invariant manifolds, geometric singular perturbation theory, the blowup method, piecewise smooth systems
My research is focused on global analysis of (low dimensional) dynamics in ordinary differential equations. In my research articles, I frequently prove existence (and uniquness/bifurcations/etc.) of limit cycles - occasionally in models coming from applications (mechanics/biology/chemistry/etc.) - using Geometric Singular Perturbation Theory (GSPT), with the blowup method as the key technical tool. This theory is relevant for the solution of Hilbert's 16 problem (on the number of limit cycles in planar polynomial systems), but my main contribution to the field has been the extension of GSPT to (a) systems with non-polynomial growth and (b) systems close to piecewise smooth ones. Future directions of my research include GSPT with complex time, with the aim to "merge" oscillatory dynamics, a previous focus area of my research, with hyperbolic dynamics. read more
Maria Montanucci, Assistant ProfessorKeywords: Algebra, Algebraic-Geometry, Algebraic Curves, Finite Fields, Coding Theory, Error-correcting Codes, Combinatorics, Galois geometries
Algebraic geometry is a branch of mathematics based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems and viceversa. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. The power of the connection between Algebra and Geometry shows itself in a number of applications. Leading examples are Coding theory and Cryptography. My research focuses on the investigation of the algebraic and geometric properties of algebraic curves that lead to good error-correcting codes as well as the construction of good curves for the purpose of error-correction. (1) Algebraic Geometry in positive characteristic (automorphism groups of algebraic curves, birational invariants, maximal curves, quotient curves), (2) Coding Theory (functional codes, AG codes, quantum codes, convolutional codes), (3) Linear sets and their applications (scattered polynomials, MRD codes). read more
Morten Brøns, Professor, Head of sectionKeywords: dynamical systems, mathematical modelling, vortex dynamics, singular perturbations, model reduction, mathematical chemistry, mathematical biology, fluid mechanics, non-linear vibrations, bifurcation theory
I work with various aspects of dynamical systems that can be modelled by non-linear differential equations, mostly ordinary differential equations. The applications span from biology and chemistry to fluid and solid mechanics. My research is currently focused on two topics: 1) Singular perturbation (or slow-fast) systems with several time scales. This includes efficient model reduction methods, where one tries to eliminate the short-term fast dynamics and mixed-mode oscillations where a limit cycle changes between small and large amplitude behavior. 2) Bifurcation theory for vortices: Developing mathematical descriptions of vortex structures in fluid flows with the special purpose of understanding the creation, interaction and merging of vortices. read more
Peter Beelen, ProfessorKeywords: algebra, discrete mathematics, algebraic varieties, finite fields, function fields, error-correcting codes
My research is in algebra with applications in discrete mathematics. The algebraic objects I study are algebraic varieties defined over a finite field, especially algebraic curves which can be described equivalently by their function fields. The study of function fields, is one of my main areas of research. The main application of algebraic varieties that I study, is within the area of algebraic coding theory. In the case of curves, these algebraic codes are known as algebraic geometry codes (AG codes). Studying properties of AG codes and finding fast decoders for them is another of my main areas of research. read more
Steen Markvorsen, ProfessorKeywords: Differential geometry, global geometric analysis, Riemannian geometry, Lorentzian geometry, Finslerian geometry
My interests are differential geometry with special emphasis on the rôle and meaning of curvature. The methods are analytic (potential theory and heat content analysis), geometric (curvature comparison geometry), and metric (Aleksandrov geometry and minimal metric graph immersions). Often via the local and global behavior of geodesic sprays. Matematicum and InterMat initiatives for high schools students. Didactically motivated applications of Computer Algebra and Geometric Analysis Systems (CAGAS) for disseminating and unfolding mathematical concepts and ideas. read more
Ole Christensen, ProfessorKeywords: functional analysis, operator theory, harmonic analysis, Fourier analysis, approximation theory, frame theory, Gabor/wavelet theory, generalized shift-invariant systems
Frame theory is a very useful tool in pure mathematics and engineering. A frame for a Hilbert space leads to an expansion of all elements in the Hilbert space that is very similar to the well-known expansion in terms of an orthonormal basis; however, the setup of a frame is much more flexible and it is much easier to design a frame with prescribed properties than for the ONB case. An important feature of frames is that they might be redundant, which makes frames very useful in signal processing. Current projects include an analysis of various operator representations for frames (exact representations and also approximate representations) as well as a generalization of classical frame theory to a theory that replaces the exact frame expansions by "approximate expansions within machine precision." read more
PhDs, Postdocs and Research Assistants
Coming soon.