Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Groups, Dynamics, and Approximation
No full textThe workshop covered a wide range of topics, with emphasis on Geometric Group Theory, Ergodic Theory and links with Functional Analysis on the one hand and Mathematical Logic on the other. The goal of the workshop was to bring together experts working in various fields, to foster interaction between them and to present some of the recent breakthroughs
Global Solutions to Stochastic Wave Equations with Superlinear Coefficients
No full textWe prove existence and uniqueness of a random field solution to a stochastic wave equation in dimensions with diffusion and drift coefficients of the form for some >0. The proof relies on a sharp analysis of moment estimates of time and space increments of the corresponding stochastic wave equation with globally Lipschitz coefficients. We give examples of spatially correlated Gaussian driving noises where the results apply
Toric Geometry
No full textToric geometry is a subfield of algebraic geometry with rich
interactions with geometric combinatorics, and many other fields of
mathematics. This workshop brought together a broad range of mathematicians interested in toric matters, and their generalizations and applications
Arbeitsgemeinschaft: Elliptic Cohomology according to Lurie
No full textIn this collection we give an overview of Jacob Lurie's construction of elliptic cohomology and Lubin Tate theory.
As opposed to the original construction by Goerss-Hopkins-Miller, which uses heavy obstruction theory, Lurie constructs these objects by a moduli problem in spectral algebraic geometry. A major part of this text is devoted to the foundations and background in higher algebra needed to set up this moduli problem (in the case of Lubin Tate theory) and prove that it is representable
The Interaction of Curvature and Topology
No full textIn this snapshot we will outline the mathematical
notion of curvature by means of comparison geometry.
We will then try to address questions as the ways in
which curvature might influence the topology of a
space, and vice versa
Surface, Bulk, and Geometric Partial Differential Equations: Interfacial, stochastic, non-local and discrete structures
No full textPartial differential equations in complex domains with free\linebreak boundaries
and interfaces continue to be flourishing research areas at the
interfaces between PDE theory, differential geometry, numerical
analysis and applications.
Main themes of the workshop have been PDEs on evolving domains, phase
field approaches, interactions of bulk and surface PDEs, curvature
driven evolution equations. Applications particular from biology, such
as cell and cancer modelling and fluid as well solid mechanics have been
subjects of the conference
Expander graphs and where to find them
No full textGraphs are mathematical objects composed of a collection
of “dots” called vertices, some of which are
joined by lines called edges. Graphs are ideal for visually
representing relations between things, and mathematical
properties of graphs can provide an insight
into real-life phenomena. One interesting property is
how connected a graph is, in the sense of how easy it
is to move between the vertices along the edges. The
topic dealt with here is the construction of particularly
well-connected graphs, and whether or not such
graphs can happily exist in worlds similar to ours
Nonlinear Hyperbolic Problems: modeling, analysis, and numerics
No full textThe workshop gathered together
leading international experts, as well as most
promising young researchers, working on the modelling, the
mathematical analysis, and the numerical methods for nonlinear
hyperbolic partial differential equations (PDEs). The meeting focussed
on addressing outstanding issues and identifying promising new
directions in all three fields, i.e.
modelling, analysis, and numerical discretization.
Key questions settled around the lack of well-posedness theories for
multidimensional systems of conservation laws and the use of hyperbolic modelling beyond
the classical topic of gas dynamics. A focal point in numerics has been
the discretization of random evolutions and uncertainty quantification.
Equally important, new multi-scale methods and schemes for asymptotic regimes
have been considered
Minimal Codimension One Foliation of a Symmetric Space by Damek-Ricci Spaces
No full textIn this article we consider solvable hypersurfaces of the form with induced metrics in the symmetric space , where a suitable unit length vector in the subgroup of the Iwasawa decomposition . Since is rank , is -dimensional and we can parametrize these hypersurfaces via an angle determining the direction of . We show that one of the hypersurfaces (corresponding to ) is minimally embedded and isometric to the non-symmetric -dimensional Damek-Ricci space. We also provide an explicit formula for the
Ricci curvature of these hypersurfaces and show that all hypersurfaces for admit planes of both negative and positive sectional curvature. Moreover, the symmetric space admits a minimal foliation with all leaves isometric to the non-symmetric -dimensional Damek-Ricci space
Logarithmic Enumerative Geometry and Mirror Symmetry
No full textThe new field of log enumerative geometry has formed at the crossroads
of mirror symmetry, Gromov-Witten theory and log geometry.
This workshop has been the first to promote this field and bring
together the junior and senior experts of this quickly evolving topic.
Spontaneous exchange, unforeseen mutual benefit as well as having each
participant give a presentation allowed for novel progress and insight