Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Homology and -Theory of Torsion-Free Ample Groupoids and Smale Spaces
No full textGiven an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the -groups of the groupoid C*-algebra when the groupoid has torsion-free stabilizers and satisfies the strong Baum–Connes conjecture. The construction is based on the triangulated category approach to the Baum–Connes conjecture by Meyer and Nest. For the unstable equivalence relation of a Smale space with totally disconnected stable sets, this spectral sequence shows Putnam’s homology groups on the second sheet
Mini-Workshop: Almost Complex Geometry (online meeting)
No full textThe mini-workshop focused on very recent developments of analytic and algebraic techniques for studying almost complex
structures which are not necessarily integrable. It provided a forum to discuss and compare techniques from PDE's, elliptic
theory, deep algebraic structures, as well as geometric flows, and new topological invariants, towards attacking several
longstanding open problems in the field of complex and almost complex geometry
Cohomology of Finite Groups: Interactions and Applications (hybrid meeting)
No full textThe cohomology of finite groups is an important tool in many subjects
including representation theory and algebraic topology.
This meeting was the fifth in a series that has emphasized the interactions
of group cohomology with other areas. In spite of the Covid-19 epidemic,
this hybrid meeting ran smoothly with about half the participants physically
present and the other half participating via Zoom
Octonion Polynomials with Values in a Subalgebra
No full textIn this paper, we prove that given an octonion algebra over a field , a subring and an octonion -algebra inside , the set of polynomials satisfying is an octonion -algebra, under the assumption that either or , and contains the standard generators of and their inverses.
The project was inspired by a question raised by Werner on whether integer-valued octonion polynomials over the reals form a nonassociative ring. We also prove that the polynomials for prime are integer-valued in the ring of polynomials over any real nonsplit Cayley-Dickson algebra
Calculus of Variations (hybrid meeting)
No full textCalculus of Variations touches several interrelated areas.
In this workshop we covered several topics, such as
minimal submanifolds, mean curvature and related flows, free boundary problems, variational
models of interacting dislocations, defects in physical
systems, phase transitions, etc
Low-dimensional Topology
No full textThe workshop brought together experts from across all areas of low-dimensional topology, including knot theory, mapping class groups, three-manifolds and four-manifolds. In addition to the standard research talks we had five survey talks by Burton, Minsky, Powell, Reid, and Roberts leading to discussions of open problems. Furthermore we had three sessions of five-minute talks by a total of thirty-five participants
Komplexe Analysis - Algebraicity and Transcendence (hybrid meeting)
No full textThis is the report of the Oberwolfach workshop Komplexe Analysis 2020. It was mainly devoted to the transcendental methods of complex algebraic geometry and featured eighteen talks about recent important developments in Hodge theory, moduli spaces, hyperbolicity, Fano varieties, algebraic foliations, algebraicity theorems for subvarieties and their applications to transcendence proofs for numbers. Two talks were more algebraic in nature and devoted to non-commutative deformations and syzygies of secant varieties
Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability
No full textContinuing the tradition initiated in the MFO workshops held in 2014 and 2017, this workshop was dedicated to the newest developments in real algebraic geometry and polynomial optimization, with a particular emphasis on free non-commutative real algebraic geometry and hyperbolic programming. A particular effort was invested in exploring the interrelations with free probability. This established an interesting dialogue between researchers working in real algebraic geometry and those working in free probability, from which emerged new exciting and promising synergies
Nonexistence of Subcritical Solitary Waves
No full textWe prove the nonexistence of two-dimensional solitary gravity water waves with subcritical wave speeds and an arbitrary distribution of vorticity. This is a longstanding open problem, and even in the irrotational case there are only partial results relying on sign conditions or smallness assumptions. As a corollary, we obtain a relatively complete classification of solitary waves: they must be supercritical, symmetric, and monotonically decreasing on either side of a central crest. The proof introduces a new function which is related to the so-called flow force and has several surprising properties. In addition to solitary waves, our nonexistence result applies to "half-solitary" waves (e.g. bores) which decay in only one direction