Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Topology of Arrangements and Representation Stability
No full textThe workshop “Topology of arrangements and representation stability” brought together two directions of research: the topology and geometry of hyperplane, toric and elliptic arrangements, and the homological and representation stability of configuration spaces and related families of spaces and discrete groups. The participants were mathematicians working at the interface between several very active areas of research in topology, geometry, algebra, representation theory, and combinatorics. The workshop provided a thorough overview of current developments, highlighted significant progress in the field, and fostered an increasing amount of interaction between specialists in areas of research
The Magic Square of Reflections and Rotations
No full textWe show how Coxeter’s work implies a bijection between complex reflection groups of rank two and real reflection groups in 0(3). We also consider this magic square of reflections and rotations in the framework of Clifford algebras: we give an interpretation
using (s)pin groups and explore these groups in small dimensions
Design and Analysis of Infectious Disease Studies
No full textThis was the fifth workshop on mathematical and statistical methods on the transmission of infectious diseases. Building on epidemiologic models which were the subject of earlier workshops, this workshop concentrated on disentangling who infected whom by analysing high-resolution genomic data of pathogens which were routinely collected during disease outbreaks. Following the trail of the small mutations which continuously occur in different places of the pathogens’ genomes, mathematical tools and computational algorithms were used to reconstruct transmission trees and contact networks
New Directions in Stochastic Optimisation
No full textRecent work in stochastic programming draws on interaction with Algebraic and Combinatorial Models, Numerical Analysis of PDEs, Risk Analysis, Mathematical Equilibrium, Minimax, and Stochastic Games. For the first time ever, the workshop brought together scholars from these fields to exchange experience and identify promising topics for future research
A short story on optimal transport and its many applications
No full textWe present some examples of optimal transport problems
and of applications to different sciences (logistics,
economics, image processing, and a little bit of
evolution equations) through the crazy story of an
industrial dynasty regularly asking advice from an
exotic mathematician
Variational Methods for the Modelling of Inelastic Solids
No full textThis workshop brought together two communities working on the same topic from different perspectives. It strengthened the exchange of ideas between experts from both mathematics and mechanics working on a wide range of questions related to the understanding and the prediction of processes in solids. Common tools in the analysis include the development of models within the broad framework of continuum mechanics, calculus of variations, nonlinear partial differential equations, nonlinear functional analysis, Gamma convergence, dimension reduction, homogenization, discretization methods and numerical simulations. The applications of these theories include but are not limited to nonlinear models in plasticity, microscopic theories at different scales, the role of pattern forming processes, effective theories, and effects in singular structures like blisters or folding patterns in thin sheets, passage from atomistic or discrete models to continuum models, interaction of scales and passage from the consideration of one specific time step to the continuous evolution of the system, including the evolution of appropriate measures of the internal structure of the system
Geometrie
No full textThe workshop Geometrie, organized by John Lott (Berkeley), André Neves (London), Iskander Taimanov (Novosibirsk) and Burkhard Wilking (Münster) was well attended with over 53 participants with broad geographic representation from all continents, and held in a very active atmosphere. During the meeting, various interesting topics in geometry were discussed, such as geometric flows, Kähler geometry, manifolds with nonnegative or positive curvature, and minimal surfaces
Interactions between Algebraic Geometry and Noncommutative Algebra
No full textThe workshop presented current developments exploring the boundaries and intersections between the fields of noncommutative algebra and representation theory on the one hand, and algebraic geometry on the other hand, with particular emphasis on topics where such interactions have led to substantial recent progress
Mathematical Methods in Quantum Chemistry
No full textThe field of quantum chemistry is concerned with the modelling and simulation of the behaviour of molecular systems on the basis of the fundamental equations of quantum mechanics. Since these equations exhibit an extreme case of the curse of dimensionality (the Schrödinger equation for N electrons being a partial differential equation on R3N ), the quantum-chemical simulation of even moderate-size molecules already requires highly sophisticated model-reduction, approximation, and simulation techniques. The workshop brought together selected quantum chemists and physicists, and the growing community of mathematicians working in the area, to report and discuss recent advances on topics such as coupled-cluster theory, direct approximation schemes in full configuration-interaction (FCI) theory, interacting Green’s functions, foundations and computational aspects of densityfunctional theory (DFT), low-rank tensor methods, quantum chemistry in the presence of a strong magnetic field, and multiscale coupling of quantum simulations
Estimating the volume of a convex body
No full textSometimes the volume of a convex body needs to
be estimated, if we cannot calculate it analytically.
We explain how statistics can be used not only to
approximate the volume of the convex body, but also
its shape