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Aktuelles
Stefan Müller erhält Lehrpreis der Universität Bonn
Lillian Pierce erhält den AWM-Sadosky Research Prize in Analysis
Mathestudium auf Probe - SchülerInnenwoche am HCM
"Mathematik zum Anfassen" - Ausstellung im Deutschen Museum Bonn in Kooperation mit dem HCM
Drei Mitglieder und Fellows des HCM sind zum ICM 2018 eingeladen
Doppelte Ehrung für Peter Scholze
HCM-Mitglied Christian Bayer ist Sprecher eines neuen Graduiertenkollegs
Universitäten Bonn und Köln gründen neues Institut
Hohe Auszeichnung für Gerd Faltings
Preise für die besten Bachelor-Absolventen und Hausdorff-Gedächtnispreis
Peter Scholze in die Akademie der Wissenschaften und der Literatur aufgenommen
Ada-Lovelace-Preis for Nora Lüthen und Sara Hahner
EMS Preis für Hausdorff Chair Peter Scholze
Sergio Conti erhält Lehrpreis 2016
Preis der Berlin-Brandenburgischen Akademie der Wissenschaften für Peter Scholze
Begehrter ERC Advanced Grant geht an Prof. Sturm
Mathematik zur Bekämpfung von Krebs
Preise für die besten Bachelor-Arbeiten und Hausdorff-Gedächtnispreis
Leibniz Preis für Hausdorff Chair Peter Scholze
Peter Scholze wird mit dem Prix Fermat 2015 ausgezeichnet
Stefan Müller und Werner Müller zu Mitgliedern der Academia Europaea gewählt
Die Zukunft genauer vorhersehen
Bonn ist Deutschlands beste Universität für Mathematik
Wolfgang Lück erhält ERC Advanced Grant
Peter Scholze erhält den Ostrowski-Preis 2015
Shaw Prize für Gerd Faltings
Peter Scholze erhält den AMS Cole Prize in Algebra
Peter Scholze erhält Clay Research Award
 
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Forschung

Als kleiner Einblick in die Breite der mathematischen Gebiete, die in Bonn vertreten sind, sind hier vier der zehn Forschungsfelder des Exzellenzclusters Hausdorff Center for Mathematics (HCM) in englischer Sprache vorgestellt. Eine vollständige Liste finden Sie auf den Seiten des HCM.

HCM Forschungsfeld 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 Research Area F*...

HCM Forschungsfeld 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 Forschungsfeld 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 Forschungsfeld 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...

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