Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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Analysis, Geometry and Topology of Singular PDE (hybrid meeting)
No full textThis is a report on the Oberwolfach conference "Analysis, geometry and topology of singular PDE'', June 2-12, 2021.
This workshop, held in an hybrid format, focused on the topology, geometry and geometric analysis of certain spaces with singularities:
stratified spaces, compactifications of moduli spaces, spaces carrying a (singular) foliation, etc., and on the microlocal techniques,
either in their classical forms or in more recent versions developed to handle singular PDE, or via the groupoid approach
Differentialgeometrie im Grossen (hybrid meeting)
No full textThe field of classical differential geometry has expanded enormously over the last several decades, helped by the development of tools from neighboring fields such as partial differential equations, complex analysis and geometric topology. In the spirit of the previous meetings in the series, this meeting will bring together researchers from apparently separate subfields of differential geometry, but whose work is linked by common themes. In particular, this meeting will emphasize intrinsic geometric questions motivated by the classification and rigidity of global geometric structures and the interaction of curvature with the underlying geometry and topology
Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (online meeting)
No full textThe central topic of the workshop was the notion of logarithmic vector fields
along a divisor in a smooth complex analytic or algebraic variety, i.e., the
vector fields on the ambient variety tangent to the divisor. Following their
introduction by K.~Saito for the purpose of studying the universal unfolding of
an isolated singularity, this fundamental object has been the focus of studies
in a wide range of mathematical fields such as algebra, algebraic geometry,
singularity theory, root systems, (geometric) representation theory, combinatorics,
(toric) topology, or symplectic geometry. In the last few years the logarithmic
vector field approach has seen some unexpected and striking advances and deep
applications. The aim of the workshop was to provide reports and to
share these various new developments in the field
Statistics of Stochastic Differential Equations on Manifolds and Stratified Spaces (hybrid meeting)
No full textStatistics for stochastic differential equations (SDEs) attempts to use SDEs as statistical models for real-world phenomena. This involves an understanding of qualitative properties of this class of stochastic processes which includes Brownian motion as well as estimation of parameters in the SDE or a nonparametric estimation of drift and diffusivity fields from observations. Observations can be in continuous time, in high frequency discrete time considering the limit of small inter-observation times or in discrete time with constant inter-obseration times. Application areas of SDEs where state spaces are naturally viewed as manifolds or stratified spaces include multivariate stochastic volatility models, stochastic evolution of shapes (e.g. of biological cells), time-varying image deformations for video analysis and phylogenetic trees
Dynamics of Waves and Patterns (hybrid meeting)
No full textThe dynamics of waves and patterns play a significant role in the sciences, especially in fluid mechanics, material science, neuroscience and ecology. The mathematical treatment interconnects several areas, ranging from evolution equations and functional analysis to dynamical systems, geometry, topology, and stochastic as well as numerical analysis. This workshop has specifically focussed on dynamic stability on extended domains, bifurcations of waves and patterns, effects of stochastic driving, and spatio-temporal inhomogenities. During the workshop, multiple new directions, collaborations, and very interesting scientific conversations arose across the entire field
Spatial Networks and Percolation (hybrid meeting)
No full textThe classical percolation problem is to find whether there is an infinite connected component in a random set created by removing edges from a -dimensional lattice, independently at random.
Since its introduction into the mathematical literature by Broadbent and Hammersley (1957) the subject of percolation has developed in many ways and is now one of the most exciting and active research areas in probability and statistical mechanics. In this workshop, we focused on current trends, including percolation on point sets with correlations,
on spatial random graphs and networks with scale-free degree distribution or long-range edge distribution, percolation of random sets like level set of Gaussian fields or the vacant set of interlacements, conformally invariant percolation structures in the plane, and random walks or information diffusion on percolation clusters. The workshop brought together more than sixty experts and promising young researchers from probability, statistical mechanics and computer science working on all aspects of percolation and spatial networks for an unprecedented exchange of new ideas and methods, with outstanding high quality online talks
Dynamische Systeme (hybrid meeting)
No full textThis workshop continued a biannual series of workshops at Oberwolfach on
dynamical systems that started with a meeting organized by Moser and Zehnder in 1981.
Workshops in this series focus on new results and developments in
dynamical systems and related areas of mathematics, with symplectic geometry playing an important role in recent years in connection with Hamiltonian dynamics. In this year special emphasis was placed on various kinds of spectra (in contact geometry, in Riemannian geometry, in dynamical systems and in symplectic topology) and their applications to dynamics
Mini-Workshop: Nonlocal Analysis and the Geometry of Embeddings (hybrid meeting)
No full textBoth self-avoidance and self-contact of geometric objects can be modeled
using repulsive energies
that separate isotopy classes.
Giving rise to nonlocal operators, they are interesting objects in their own right.
Moreover, their analytical structure allows for devising
numerical schemes enjoying robust features such as
energy stability.
This workshop aimed at discussing recent trends in this
matter, including potential applications to modeling
The Pelletier-Ressayre Hidden Symmetry for Littlewood-Richardson Coefficients
No full textWe prove an identity for Littlewood–Richardson coefficients conjectured by Pelletier and Ressayre. The proof relies on a novel birational involution defined over any semifield
Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (hybrid meeting)
No full textThe talks at the workshop and the research done during the week focused on aspects of algebraic geometry in the broad sense. Special emphasis was put on hyperkähler manifolds and derived categories