Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Mini-Workshop: Numerical Analysis for Non-Smooth PDE-Constrained Optimal Control Problems
No full textThis mini-workshop brought together leading experts working on various aspects of numerical analysis for optimal control problems with nonsmoothness. Fifteen extended abstracts summarize the presentations at this mini-workshop
Mini-Workshop: Superexpanders and Their Coarse Geometry
No full textIt is a deep open problem whether all expanders are superexpanders. In fact, it was already a major challenge to prove the mere existence of superexpanders. However, by now, some classes of examples are known: Lafforgue’s expanders constructed as sequences of finite quotients of groups with strong Banach property (T), the examples coming from zigzag products due to Mendel and Naor, and the recent examples coming from group actions on compact manifolds. The methods which are used to construct superexpanders are typically functional analytic in nature, but also rely on arguments from geometry and combinatorics. Another important aspect of the study of superexpanders is their (coarse) geometry, in particular in order to distinguish them from each other. The aim of this workshop was to bring together researchers working on superexpanders and their coarse geometry from different perspectives, with the aim of sharing expertise and stimulating new research
Quadratic Forms and Related Structures over Fields
No full textThe range of topics discussed at the workshop “Quadratic Forms and Related Structures over Fields” included core themes from the algebraic theory of quadratic and hermitian forms and their Witt groups, several aspects of the theory of linear algebraic groups and homogeneous varieties, cohomological invariants as well as some arithmetic aspects pertaining to the theory of quadratic forms over certain types of ground fields, e.g., function fields
Exceptional Legendrian Torus Knots
No full textWe present classification results for exceptional Legendrian realisations of torus knots. These are the first results of that kind for non-trivial topological knot types. Enumeration results of Ding-Li-Zhang concerning tight contact structures on certain Seifert fibred manifolds with boundary allow us to place upper bounds on the number of tight contact structures on the complements of torus knots; the classification of exceptional realisations of these torus knots is then achieved by exhibiting suffciently many realisations in terms of contact surgery diagrams. We also discuss a couple of general theorems about the existence of exceptional Legendrian knots
Deformation Classification of Real Non-Singular Cubic Threefolds with a Marked Line
No full textResearch in Pairs 2017We prove that the space of pairs formed by a real non-singular cubic hypersurface with a real line has 18 connected components and give for them several quite explicit interpretations. The first one relates these components to the orbits of the monodromy action on the set of connected components of the Fano surface formed by real lines on . For another interpretation we associate with each of the 18 components a well defined real deformation class of real non-singular plane quintic curves and show that this deformation class together with the real deformation class of characterizes completely the component.Research in Pairs 201
Reactive Flows in Deformable, Complex Media
No full textMany processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is changing in time, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, material science, or biological systems.The emerging mathematical models account for various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. The focus in this workshop was on novel techniques and ideas in the mathematical modelling, analysis, the numerical discretization and the upscaling of problems as described above
Free Probability Theory
No full textThe workhop brought together leading experts, as well as promising young researchers, in areas related to recent developments in free probability theory. Some particular emphasis was on the relation of free probability with random matrix theory
Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory
No full textFrames are collections of vectors in a Hilbert space which have reconstruction properties similar to orthonormal bases and applications in areas such as signal and image processing, quantum information theory, quantization, compressed sensing, and phase retrieval. Further desirable properties of frames for robustness in these applications coincide with structures that have appeared independently in other areas of mathematics, such as special matroids, Gel’Fand-Zetlin polytopes, and combinatorial designs. Within the past few years, the desire to understand these structures has led to many new fruitful interactions between frame theory and fields in pure mathematics, such as algebraic and symplectic geometry, discrete geometry, algebraic combinatorics, combinatorial design theory, and algebraic number theory. These connections have led to the solutions of several open problems and are ripe for further exploration. The central goal of our mini-workshop was to attack open problems that were amenable to an interdisciplinary approach combining certain subfields of frame theory, geometry, and combinatorics
A McKay Correspondence for Reflection Groups
No full textWe construct a noncommutative desingularization of the discriminant of a finite reflection group as a quotient of the skew group ring . If is generated by order two reflections, then this quotient identifies with the endomorphism ring of the reflection arrangement viewed as a module over the coordinate ring of the discriminant of . This yields, in particular, a correspondence between the nontrivial irreducible representations of to certain maximal Cohen--Macaulay modules over the coordinate ring . These maximal Cohen--Macaulay modules are precisely the nonisomorphic direct summands of the coordinate ring of the reflection arrangement viewed as a module over . We identify some of the corresponding matrix factorizations, namely the so-called logarithmic co-residues of the discriminant
Cohomological and Metric Properties of Groups of Homeomorphisms of R
No full textIn recent years, the family of groups sharing features or design principles with classical Thompson groups has grown considerably. The workshop highlights new developments in this field with special emphasis on algorithmic questions, cohomological properties, and smoothability of actions