Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Aeppli-Bott-Chern-Massey Products, Bigraded Notions of Formality, and Non-Zero Degree Maps
No full textWe introduce and study notions of bigraded formality for the algebra of forms on a complex manifold, along with their relation to higher Aeppli-Bott-Chern-Massey products which extend, in an augmented setting, the case of triple products studied by Angella-Tomassini. We show that these Aeppli-Bott-Chern-Massey products on complex manifolds pull back non-trivially to the blow-up along a complex submanifold, as long their degree is less than the real codimension of the submanifold. We then consider the general question of under which conditions formality is preserved by non-zero degree maps
Interpolation, Approximation, and Algebra
No full textThis report involves two concepts of geometric modeling: multi-variate data interpolation by polynomials, and the study of generalized bary\-centric coordinates. These topics are connected to a wide range of of applications, from computer aided design (CAD) systems for designing airplanes and automobiles to animation in movies to problems in numerical analysis and partial differential equations. Traditionally these topics were studied mostly from an analytic standpoint, but recently advanced algebraic tools have come into the picture. The purpose of the mini-workshop was to bring together a diverse group of researchers with different areas of expertise, drawing from both the approximation theory and algebraic geometry communities, and to explore the connections between the two areas in greater detail
Geometrie
No full textThe workshop Geometrie, organized by Aaron Naber (Evanston),
André Neves (Chicago) and Burkhard Wilking (Münster) was well attended with over 42 participants (35 in person and 7 online) with broad geographic representation from all continents, and held in a very active atmosphere. During the meeting, various interesting topics in geometry were discussed, such as geometric flows, Einstein manifolds and spaces with sectional curvature bounds
Topologie
No full textThe lectures in the workshop covered various topics in modern topology, including algebraic and geometric topology, homotopy theory, geometric group theory, and manifold topology, as well as connections to neighboring areas, most prominently symplectic topology/geometry. The following current research topics received more attention during the workshop: manifolds and K-theory, symplectic topology and Floer homology, generalizations of hyperbolic techniques in geometric group theory, and equivariant and motivic homotopy theory. The aim of the various topics was to foster communication and provide chances for participants to see and experience driving questions and important methods in nearby fields within the realm of topology
Arbeitsgemeinschaft: Quantitative Stochastic Homogenization
No full textHomogenization means approximating the effective, i.e. macroscopic, behavior of
a heterogeneous medium by a homogeneous one, which amounts to a substantial conceptual
and practical reduction of complexity.
Stochastic homogenization means that one is considering an ensemble of,
i.e. a probability measure on, such heterogeneities (typically expressing a lack
of knowledge of the details); and that the effective behavior is also deterministic next to being homogeneous. The aim of this Arbeitsgemeinschaft is to present the recent progress in this field
What is pattern?
No full textPattern is ubiquitous and seems totally familiar. Yet if we ask what it is, we find a bewildering collection of answers. Here we suggest that there is a common thread, and it revolves around dynamics
Mini-Workshop: Subvarieties in Projective Spaces and Their Projections
No full textThe major goals of this workshop are to lay paths for a
systematic study of geproci (and related, e.g., projecting to almost
complete intersections or full intersections) sets of points in
projective spaces, study algebraic properties of their ideals (e.g.
in the spirit of the Cayley-Bacharach properties), and to identify
the most promising new directions for study
Convolution in Dual Cesàro Sequence Spaces
No full textWe investigate convolution operators in the sequence spaces , for 1 ces_pd_pd_pl^{p}$
Hilbert Complexes: Analysis, Applications, and Discretizations
No full textIn this workshop 70 (43 at MFO, 27 online) leading mathematicians from Europe, United States, China, and Australia
met at the MFO to discuss and present new developments
in the mathematical and numerical analysis including discretizations
of Hilbert complexes related to systems of partial differential equations,
in particular the well known de Rham complex
and the complexes of elasticity and the biharmonic equations.
The report at hand offers the extended abstracts of their talks
Mini-Workshop: A Geometric Fairytale full of Spectral Gaps and Random Fruit
No full textIn many situations, most prominently in quantum mechanics, it
is important to understand well the eigenvalues and associated
eigenfunctions of certain self-adjoint differential operators. The goal
of this workshop was to study the strong link between spectral
properties of such operators and the underlying geometry which might
be randomly generated. By combining ideas and methods from
spectral geometry and probability theory, we hope to stimulate new
research including important topics such as Bose--Einstein condensation
in random environments