Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Mathematical Advances in Geophysical Fluid Dynamics (online meeting)
No full textThis workshop on "Mathematical Advances in Geophysical Fluid Dynamics" was organized as an online seminar and addressed recent advances in analytical, modeling and computational studies of
geophysical fluid models.
Of particular interest were the contributions concerning modeling and computation of sea-ice models, well-posedness results for the primitive equations, internal waves for stratified flows
and models for moist atmospheric dynamics including phase transitions
Mini-Workshop: One-sided and Two-sided Stochastic Descriptions
No full textWe consider the set of discrete time stochastic processes which are dependent on their past, and the set of those that depend on both their past and their future. As long as we only allow dependence on a finite number of variables, those two sets are the same. However interesting questions appear when the dependence becomes infinite, and some of them were discussed during our mini-workshop
Classical and Quantum Mechanical Models of Many-Particle Systems (online meeting)
No full textThe collective behaviour of many-particle systems is a common denominator in the challenges of a highly diverse range of applications: from classical problems in Physics (gas dynamics e.g. Boltzmann's equation, plas\-ma dynamics e.g. various Vlasov equations, semiconductors, quantum mechanics) to current models in biology (kinetic models for collective interaction e.g. swarming, evolution of trait-structured species) to rising topics in social sciences (opinion formation, crowding phenomena) and economics (wealth distribution, mean-field games).\\
Key mathematical questions concern the analysis (global-in-time wellposedness, regularity), rigorous scaling resp. macroscospic limits (model reduction from many-particle models to mean-field/mesoscopic descriptions to macroscopic evolutions), efficient and asymptotic preserving numerical methods and qualitative results (e.g. large-time equilibration)
Mini-Workshop: Cohomology of Hopf Algebras and Tensor Categories
No full textThe mini-workshop featured some open questions
about the cohomology of Hopf algebras
and tensor categories.
Questions included whether the cohomology ring
of a finite dimensional Hopf algebra or a finite tensor category is
finitely generated, questions about corresponding
geometric methods in representation theory, and
questions about noetherian Hopf algebras.
The workshop brought together mathematicians currently
working on these and other open problems
Matchings and Squarefree Powers of Edge Ideals
No full textSquarefree powers of edge ideals are intimately related to matchings of the underlying graph. In this paper we give bounds for the regularity of squarefree powers of edge ideals, and we consider the question of when such powers are linearly related or have linear resolution. We also consider the so-called squarefree Ratliff property
Congruences Associated with Families of Nilpotent Subgroups and a Theorem of Hirsch
No full textOur main result associates a family of congruences with each suitable system of nilpotent subgroups of a finite group. Using this result, we complete and correct the proof of a theorem of Hirsch concerning the class number of a finite group of odd order
Random permutations
No full text100 people leave their hats at the door at a party and
pick up a completely random hat when they leave.
How likely is it that at least one of them will get
back their own hat? If the hats carry name tags,
how difficult is it to arrange for all hats to be returned
to their owner? These classical questions of
probability theory can be answered relatively easily.
But if a geometric component is added, answering
the same questions immediately becomes very hard,
and little is known about them. We present some
of the open questions and give an overview of what
current research can say about them
Formation Control and Rigidity Theory
No full textFormation control is one of the fundamental coordination
tasks for teams of autonomous vehicles. Autonomous
formations are used in applications ranging
from search-and-rescue operations to deep space
exploration, with benefits including increased robustness
to failures and risk mitigation for human operators.
The challenge of formation control is to develop
distributed control strategies using vehicle onboard
sensing that ensures the desired formation is
obtained. This snapshot describes how the mathematical
theory of rigidity has emerged as an important
tool in the study of formation control problems
Subfactors and Applications
No full textThe theory of subfactors connects diverse topics in mathematics
and mathematical physics such as tensor categories, vertex operator
algebras, quantum groups, quantum topology, free probability,
quantum field theory, conformal field theory,
statistical mechanics, condensed matter
physics and, of course, operator algebras.
We invited an international group of researchers from these areas
and many fruitful interactions took place during the workshop
Differentialgeometrie im Grossen
No full textThe topics discussed at the meeting reflected current trends in global differential geometry. These topics included complex geometry, Einstein metrics, geometric flows, metric geometry and manifolds satisfying curvature bounds