One Two
Three new Bonn Junior Fellows at HCM
Fields Medal for Peter Scholze
Thoralf Räsch received a teaching award of the University of Bonn
Peter Scholze new director at the Max Planck Institute for Mathematics
Faster computer chips via graph theory
Geordie Williamson elected Fellow of the Royal Society
Jens Frehse received Golden Commemorative Medal
HCM supports Germany's first girls' team at the European Girls' Mathematical Olympiad together with IBM
Sloan Research Fellowship awarded to Lillian Pierce and Joe Neeman
Lisa Hartung has been awarded the DMV "Fachgruppe Stochastik" prize
Patrik Ferrari receives the first Alexanderson Award
Awards for best bachelor degrees and Hausdorff Memorial Prize
State Secretary Storsberg visits HCM
Closer to the optimal tour - Bonn mathematicians are honored for a new algorithm in "traveling salesman problem"
Clelia Albrecht received Ada Lovelace Prize
GlobalMathNetwork - A worldwide network in mathematics
Germany's Excellence Strategy: HCM has cleared the first hurdle
Christoph Thiele is the new director of the Hausdorff Research Institute for Mathematics (HIM)
Shanghai Ranking: Bonn's economists and mathematicians at the top
Stefan Müller receives a teaching award from the University of Bonn
Lillian Pierce wins the AWM-Sadosky Research Prize in Analysis
High school students explore maths studies
"Mathematik zum Anfassen" - Hands-on exhibition at "Deutsches Museum Bonn" in cooperation with HCM
Three HCM members and fellows invited to ICM 2018
Double honor for Peter Scholze
HCM member Christian Bayer is spokesperson of a new Research Training Group
Universities Bonn and Cologne found new institute
High honor for Gerd Faltings
Awards for best bachelor degrees and Hausdorff Prize
Ada Lovelace Prize for Nora Lüthen and Sara Hahner
EMS Prize for Hausdorff Chair Peter Scholze
Academic teaching award for Sergio Conti
Prize of the Berlin-Brandenburgische Akademie der Wissenschaften for Peter Scholze
ERC Advanced Grant for HCM coordinator Karl-Theodor Sturm
Mathematics for fighting cancer
Awards for best bachelor degrees and Hausdorff Prize
Leibniz Price for Hausdorff Chair Peter Scholze
Peter Scholze receives the Prix Fermat 2015
Stefan Müller and Werner Müller elected as members of Academia Europaea
Foreseeing the future more exactly
Bonn is the best German university for Mathematics
Wolfgang Lück receives ERC Advanced Grant
Shaw Prize awarded to Gerd Faltings
Peter Scholze receives the Ostrowski Prize 2015
Peter Scholze receives AMS Cole Prize in Algebra
Peter Scholze receives Clay Research Award
You are here: Home Research


Find below, as a small sample of the variety of mathematical research represented in Bonn, four of the ten research areas in the Hausdorff Center for Mathematics (HCM). A full list is found on HCM's webpages.

HCM Research Area F*: ‘Structures and invariants in algebra and topology’

ra-f_.jpg-This is a new research area formed by researchers, half of whom came to Bonn after the cluster started. The research area also reflects a new emphasis in topology and representation theory.

The activities of this research area aim at the interplay of geometry, topology, algebra and group theory. The topics range over

  • the classification of manifolds,
  • algebraic K- and L-theory of group rings,
  • the geometry and homology of mapping class groups,
  • equivariant and global homotopy theory,
  • and categorification of knot invariants and group algebras.

They have in common that they lead to explicit invariants in geometry and topology, designed to answer specific questions and solve specific problems, and to a better and deeper understanding of important general structures, which are of basic fundamental interest and will open the door to new projects and proofs. The investigators are experts in different fields; their respective backgrounds and expertise will lead to a fruitful cooperation and an exchange of knowledge and techniques.

Homepage of HCM Reseach Area F*...

HCM Research Area B: ‘Shape, pattern and partial differential equations’

ra-b.jpg-The interplay of the concepts of shape (interfaces in materials or geometric contours in images) and pattern (microstructures in materials or textures in images) characterises mathematical models both in the natural sciences and in computer vision and imaging. This Research Area capitalises on the similarity of the mathematical tools involved: differential geometry, the calculus of variations, and nonlinear partial differential equations. Examples of this fruitful interplay are the rigorous understanding of

  • lower dimensional elasticity theories,
  • multiscale models bridging between statistical physics and continuum mechanics,
  • pattern formation and interface dynamics in biological models, or
  • the combination of Riemannian geometry and continuum mechanics in shape space theory.

Research in this area emphasises the understanding of concrete phenomenons in connection to challenging applications over the development of abstract theory. Furthermore, we aim at developing fast and reliable numerical algorithms in a close interplay with modeling and analysis.

Homepage of HCM Research Area B...

HCM Research Area J: ‘High-Dimensional problems and multi-scale methods’

ra-j.jpg-Mathematical modelling of physical phenomena often leads to high-dimensional partial differential equations. Examples are the many particle Schrödinger equation in quantum physics, the description of queueing networks, reaction mechanisms in molecular biology, visco-elasticity in polymer fluids, or models for the pricing of financial derivatives. Also, homogenisation and stochastic modelling usually result in high-dimensional PDEs. Typically, besides their high dimension, these problems involve multiple scales in space and time. In this Research Area we deal with high-dimensional problems and multiscale methods from the perspective of modelling, analysis, and numerical simulation. In the numerical treatment, the so-called curse of dimension is encountered. The computational cost required for an approximate solution scales exponentially with the dimension of the problem, and thus renders classical numerical approaches useless in practise. Therefore, the Research Area focuses on:

  • Dimension-independent discretisation and solution methods
  • Simplified effective models and their macroscopic behaviour of large high-dimensional systems.

Homepage of HCM Research Area J

HCM Research Area KL: ‘Algorithms, combinatorics, and complexity’

ra-kl.jpg-The interaction between mathematics and computation, and more specifically between optimization and complexity, is central in our research area. Mathematical methods are employed to devise and analyze algorithms, and algorithmic ideas are applied in mathematical domains. On the one hand, efficient algorithms for various key problems are designed in this Research Area; for example in combinatorial optimisation and number theory, some of which had been considered hitherto to be computationally intractable. On the other hand, recent years have witnessed dramatic progress in our understanding of the phenomena of efficient computation: new and deep techniques for establishing intrinsic intractability barriers, and new means for surmounting them. In most cases, some combinatorial structure needs to be explored to gain insight. Notions of efficient computation and complexity are also evolving into central paradigms in mathematics and its foundations. In a worldwide unique industrial cooperation, this Research Area develops mathematical foundations and algorithms for designing next-generation computer chips, the most complex structures that mankind has ever developed.

Homepage  of HCM Research Area KL...

Document Actions