Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Trivial Source Character Tables of SL2(q)
No full textWe compute the trivial source character tables (also called species tables of the trivial source ring) of the infinite family of finite groups SL(2,q) over a large enough field of positive characteristic via character-theoretical methods in the cases in which is odd, when~ is odd, and when
Closed geodesics on surfaces
No full textWe consider surfaces of three types: the sphere, the torus, and many-holed tori. These surfaces naturally admit geometries of positive, zero, and negative curvature, respectively. It is interesting to study straight line paths, known as geodesics, in these geometries. We discuss the issue of counting closed geodesics; this is particularly rich for hyperbolic (negatively curved) surfaces
Data Assimilation - Mathematical Foundation and Applications
No full textThe field of "Data Assimilation'' has been driven by applications from the
geosciences where complex mathematical models are interfaced with
observational data in order to improve model forecasts. Mathematically,
data assimilation is closely related to filtering and smoothing on the
one hand and inverse problems and statistical inference on the
other. Key challenges of data assimilation arise from the
high-dimensionality of the underlying models, combined with systematic
spatio-temporal model errors, pure model uncertainty quantification and
relatively sparse observation networks. Advances in the field of data
assimilation will require combination of a broad range of mathematical
techniques from differential equations, statistics, machine learning, probability, scientific computing
and mathematical modeling, together with insights from practitioners in the field.
The workshop brought together a collection of scientists
representing this broad spectrum of research strands
Mathematical Advances in Geophysical Fluid Dynamics
No full textThe workshop "Mathematical Advances in Geophysical Fluid Dynamics" addressed recent advances in modeling, analytical, computational and stochastical studies of geophysical flows.
Of particular interest were contributions concerning modeling and analysis of sea ice models, well-posedness results for the primitive equations and boundary layers, stratified flows and
models for moist atmospheric dynamics including phase transitions
Universality: Random Matrices, Random Geometry and SPDEs
No full textThe postulate that large random systems can be described by limiting
objects whose characteristic do not depend on the exact details of the
models one started from is central in probability theory, under the
name of universality. This workshop was aimed at uncovering the latest
developments of this concept in the various topics where it is
relevant, namely statistical physics, stochastic partial differential
equations, random geometries and random matrices. It was in particular
the occasion to feature some important recently introduced universal objects like the
stochastic quantization of the Yang-Mills measure in dimensions 2 and
3, the KPZ fixed point, Liouville quantum gravity metrics and other
objects connected to the Gaussian free field
Structure-Preserving Discretizations for Nonlinear Systems of Hyperbolic, Involution-Constrained Partial Differential Equations on Manifolds
No full textThe topic of this workshop was the study of mathematical and numerical analysis for involution-constrained hyperbolic partial differential equations on manifolds. An example is the positivity of the density for the compressible Euler equations. 25 international participants attended the workshop. There were 22 lectures, covering a wide gamut of the topic
Graph Theory
No full textGraph theory is a quickly developing area of mathematics,
with an increasing number of connections to various parts of
mathematics and computer science.
The workshop aimed at bringing together a broad range of researchers
at various career stages to discuss recent exciting developments,
in particular, the Product Structure Theorem and
progress towards the resolution of Hadwiger's Conjecture.
While the workshop was impacted by the COVID pandemic,
it still offered many interesting talks, which updated its participants
on recent developments covering the whole breadth of graph theory, and
collaboration opportunities
Local and Global Canonical Forms for Differential-Algebraic Equations with Symmetries
No full textLinear time-varying differential-algebraic equations with symmetries are studied. The structures that we address are self-adjoint and skew-adjoint systems. Local and global canonical forms under congruence are presented and used to classify the geometric properties of the flow associated with the differential equation as symplectic or generalized orthogonal flow. As applications, the results are applied to the analysis of dissipative Hamiltonian
systems arising from circuit simulation and incompressible flow
Real Analysis, Harmonic Analysis and Applications
No full textThe workshop focused on important developments
within the last few years in real and
harmonic analysis including nonlinear Carleson theorems
and singular integral theory, Fourier restriction theory
and spherical maximal functions as well as concurrent progress in the
application of these for example to partial differential equations
The Renormalization Group
No full textThe renormalization group was originally introduced as a multiscale approach to quantum field theory and the theory of critical phenomena, explaining in particular the universality observed e.g. in critical exponents. Over the years it has become a powerful tool in the mathematical analysis of systems with infinitely many interacting degrees of freedom. Its applications include quantum field theories, classical and quantum statistical mechanics, (stochastic) partial differential equations, operator theory, and probability theory. For some important problems, it is the only known tool for mathematical proofs. The last few years have seen further important developments, in particular in the application of the method to probabilistic questions, and to equilibrium and non-equilibrium quantum statistical mechanics.
This workshop has given an account of the most important new developments in the last five years, including methodical progress, current applications, relations to other approaches, and identified new challenges that may be tackled in future work with the help of the renormalization group