Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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Data assimilation: mathematics for merging models and data
No full textWhen you describe a physical process, for example,
the weather on Earth, or an engineered system, such
as a self-driving car, you typically have two sources of
information. The first is a mathematical model, and
the second is information obtained by collecting data.
To make the best predictions for the weather, or most
effectively operate the self-driving car, you want to
use both sources of information. Data assimilation
describes the mathematical, numerical and computational
framework for doing just that
New Trends in Teichmüller Theory and Mapping Class Groups
No full textIn this workshop, various topics in Teichmüller theory and mapping class groups were discussed. Twenty-three talks dealing with classical topics and new directions in this field were given. A problem session was organised on Thursday, and we compiled in this report the problems posed there
Complexity Theory
No full textComputational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness, and quantum computation. Many of the developments are related to diverse mathematical fields such as algebraic geometry, combinatorial number theory, probability theory, representation theory, and the theory of error-correcting codes
Homogenization of a nonlinear monotone problem with nonlinear Signorini boundary conditions in a domain with highly rough boundary
No full textWe consider a domain , , with a very rough boundary depending on~. For instance, if the domain has the form of a brush with an -periodic distribution of thin cylinders with fixed height and a small diameter of order . In a nonlinear monotone problem with nonlinear Signorini boundary conditions, depending on , on the lateral boundary of the cylinders is considered. We study the asymptotic behavior of this problem, as vanishes, i.e. when the number of thin attached cylinders increases unboundedly, while their cross sections tend to zero. We identify the limit problem which is a nonstandard homogenized problem. Namely, in the region filled up by the thin cylinders the limit problem is given by a variational inequality coupled to an algebraic system
Computing with symmetries
No full textGroup theory is the study of symmetry, and has many
applications both within and outside mathematics.
In this snapshot, we give a brief introduction to symmetries,
and how to compute with them
Max-Linear Models on Infinite Graphs Generated by Bernoulli Bond Percolation
No full textWe extend previous work of max-linear models on finite directed acyclic graphs to infinite graphs, and investigate their relations to classical percolation theory. We formulate results for the oriented square lattice graph and nearest neighbor bond percolation. Focus is on the dependence introduced by this graph into the max-linear model. As a natural application we consider communication networks, in particular, the distribution of extreme opinions in social networks
Challenges in Optimal Control of Nonlinear PDE-Systems
No full textThe workshop focussed on various aspects of optimal control problems for systems of nonlinear partial differential equations. In particular, discussions around keynote presentations in the areas of optimal control of nonlinear/non-smooth systems, optimal control of systems involving nonlocal operators, shape and topology optimization, feedback control and stabilization, sparse control, and associated numerical analysis as well as design and analysis of solution algorithms were promoted. Moreover, also aspects of control of fluid structure interaction problems as well as problems arising in the optimal control of quantum systems were considered
Computational Engineering
No full textThis Workshop treated a variety of finite element methods and applications in computational engineering and expanded their mathematical foundation in engineering analysis. Among the 53 participants were mathematicians and engineers with focus on mixed and nonstandard finite element schemes and their applications
Affine Space Fibrations
No full textWe discuss various aspects of affine space fibrations. Our interest will be focused in the singular fibers, the generic fiber and the propagation of properties of a given smooth special fiber to nearby fibers
Explicit Methods in Number Theory
No full textThe aim of the series of Oberwolfach meetings on ‘Explicit methods in number theory’ is to bring together people attacking key problems in number theory via techniques involving concrete or computable descriptions. Here, number theory is interpreted broadly, including algebraic and analytic number theory, Galois theory and inverse Galois problems, arithmetic of curves and higher-dimensional varieties, zeta and L-functions and their special values, modular forms and functions. The meeting provides a forum for presenting new methods and results on concrete aspects of number theory. Considerable attention is paid to computational issues, but the emphasis is on aspects that are of interest to the pure mathematician. In this respect the meetings differ from virtually all other computationally oriented meetings in number theory (most notably the ANTS series), which have a tendency to place actual implementations, numerical results, and cryptographic implications in the foreground. The 2018 meeting featured a mini-course on nonabelian Chabauty theory, so several of the talks were on this topic; the other talks covered a broad range of topics in number theory