Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Mathematical Aspects of Hydrodynamics
No full textThe workshop dealt with the partial differential equations that describe fluid motion and related topics.
These topics included both inviscid and viscous fluids in two and three dimensions. Some talks addressed
aspects of fluid dynamics such as the construction of wild weak solutions, compressible shock formation,
inviscid limit and behavior of boundary layers, as well as both polymer/fluid and structure/fluid interaction
Computational Multiscale Methods
No full textMany physical processes in material sciences or geophysics are characterized by inherently complex interactions across a large range of non-separable scales in space and time. The resolution of all features on all scales in a computer simulation easily exceeds today's computing resources by multiple orders of magnitude. The observation and prediction of physical phenomena from multiscale models, hence, requires insightful numerical multiscale techniques to adaptively select relevant scales and effectively represent unresolved scales. This workshop enhanced the development of such methods and the mathematics behind them so that the reliable and efficient numerical simulation of some challenging multiscale problems eventually becomes feasible in high performance computing environments
Deep Learning and Inverse Problems
No full textBig data and deep learning are modern buzz words
which presently infiltrate all fields of science and technology.
These new concepts are impressive in terms
of the stunning results they achieve for a large variety
of applications. However, the theoretical justification
for their success is still very limited. In this snapshot,
we highlight some of the very recent mathematical
results that are the beginnings of a solid theoretical
foundation for the subject
Statistical Methodology and Theory for Functional and Topological Data
No full textThe workshop focuses on the statistical analysis of complex data which cannot be represented as realizations of finite-dimensional random vectors. An example of such data are functional data. They arise in a variety of climate, biological, medical, physical and engineering problems, where the observations can be represented by curves and surfaces. Fast advances in technology continuously produce a deluge of bigger data with even more complex structures such as arteries in the brain, bones of a human body or social networks. This has sparked enormous interest in more general statistical problems where the random observations are elements of abstract topological spaces.
The workshop will stimulate development of new statistical methods for these types of data and will be an ideal platform for discussing their theoretical properties (e.g. asymptotic optimality), computational performance, and new exciting applications in areas such as machine learning, image analysis, biometrics and econometrics
Representations of Finite Groups
No full textThe workshop Representations of Finite Groups was organised by Joseph Chuang (London), Meinolf Geck (Stuttgart), Radha Kessar (London) and Gabriel Navarro (Valencia). It covered a wide variety of aspects of representation theory of finite groups and its relations to other areas of mathematics
On radial basis functions
No full textMany sciences and other areas of research and applications
from engineering to economics require the approximation
of functions that depend on many variables.
This can be for a variety of reasons. Sometimes
we have a discrete set of data points and we
want to find an approximating function that completes
this data; another possibility is that precise
functions are either not known or it would take too
long to compute them explicitly. In this snapshot
we want to introduce a particular method of approximation
which uses functions called radial basis functions.
This method is particularly useful when approximating
functions that depend on very many variables.
We describe the basic approach to approximation
with radial basis functions, including their computation,
give several examples of such functions and
show some applications
Contemporary Coding Theory
No full textCoding Theory naturally lies at the intersection of a large number
of disciplines in pure and applied mathematics. A multitude of
methods and means has been designed to construct, analyze, and
decode the resulting codes for communication. This has suggested to
bring together researchers in a variety of disciplines within
Mathematics, Computer Science, and Electrical Engineering, in order
to cross-fertilize generation of new ideas and force global
advancement of the field. Areas to be covered are Network Coding,
Subspace Designs, General Algebraic Coding Theory, Distributed
Storage and Private Information Retrieval (PIR), as well as
Code-Based Cryptography
C*-Algebras
No full textThe subject of Operator Algebras is a flourishing broad area of mathematics which has strong ties to many other areas in mathematics including Functional/Harmonic Analysis, Topology, (non-commutative) Geometry, Geometric Group Theory, Dynamical Systems, Descriptive Set Theory, Model Theory, Random Matrices and many more. The goal of the Oberwolfach meeting is to give its participants a global view of the subject to maintain and strengthen contacts between researchers from these different directions, making it possible for the most important developments and techniques to be disseminated
Heat Kernels, Stochastic Processes and Functional Inequalities
No full textThe aims of the 2019 workshop 'Heat Kernels, Stochastic Processes and Functional Inequalities' were: (a) to provide a forum to review recent progresses in a wide array of areas of analysis (elliptic, subelliptic and parabolic differential equations, transport, functional inequalities), geometry (Riemannian and sub-Riemannian geometries, metric measure spaces, geometric analysis and curvature), and probability (Brownian motion, Dirichlet spaces, stochastic calculus and random media) that have natural common interests, and (b) to foster, encourage and develop further interactions and cross-fertilization between these different directions of research
The Becker-Gottlieb Transfer: a Geometric Description
No full textIn this note, we examine geometric aspects of the Becker-Gottlieb transfer in terms of the Umkehr and index maps, and rework some classic index theorems, using the cohomological formulae of the Becker-Gottlieb transfer. The results are natural from the homotopy-theoretic point of view; they reveal subtle geometric information in the Umkehr map, and demonstrate the beauty of the Atiyah-Singer index theorem for families and its generalizations