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Mini-Workshop: The Pisot Conjecture - From Substitution Dynamical Systems to Rauzy Fractals and Meyer Sets
This mini-workshop brought together researchers with diverse backgrounds and a common interest in facets of the Pisot conjecture, which relates certain properties of a substitution to dynamical properties of the associated subshift.
Algebraische Zahlentheorie
The workshop brought together researchers from Europe, the US and Japan, who reported on various recent developments in algebraic number theory and related fields. Dominant themes were p-adic methods, L-functions and automorphic forms but other topics covered a very wide range of algebraic number theory.
Mini-Workshop: Geometric Measure Theoretic Approaches to Potentials on Fractals and Manifolds
The workshop brought together researchers and graduate students from different areas of mathematics, such as analysis, probability theory, geometry, and number theory. The topics of joint interest were motivated by recent problems in potential theory with impacts into these areas: • discrete approximation to energy minimising measures • potential theory on fractals and manifolds • geometric measure theory on fractals • probabilistic potential theory • spectral theory on fractals and sets with fractal boundary. The format of a mini-workshop was especially well-suited for our subject, since it allowed enough time for personal discussions besides the talks given by the participants. The concept of energy of a charge distribution on a subset of Euclidean space is one of the core subjects of potential theory. Recent generalisations of this concept to hyper-singular energy kernels and discrete N –point distributions exhibit a close connection with ideas from geometric measure theory. A recent article by two of the organisers shows that N –point configurations minimising the discrete energy in the hyper-singular case can be used to characterise the Hausdorff measure on d–dimensional d–rectifiable manifolds embedded in Euclidean space. Such minimal energy point sets can be used for the discretisation of manifolds, which has numerous applications. On the other hand discretisation by graph structures is a common means for analysis on fractal structures. Usually, a diffusion and an associated Laplace operator are defined by rescaling discrete random walks and their transition operators on the approximating graphs.
Algebraic K-Theory and Motivic Cohomology
Algebraic K-theory and the related motivic cohomology are a systematic way of producing invariants for algebraic or geometric structures. Its definition and methods are taken from algebraic topology, but it has also proved particularly fruitful for problems of algebraic geometry, number theory or quadratic forms. 19 one-hour talks presented a wide range of results on K-theory itself and applications. We had a lively evening session trading questions and discussing open problems.
Mini-Workshop: Theory and Numerics of Fluid-Solid Interaction
This volume contains the abstracts of a series of talks given at a mini-workshop in Oberwolfach on the theory and numerics of continuum mechanical fluid-solid/structure interaction. The characteristics of these coupled multi-field problems are that the displacement of the solid/structure has a direct influence on the surrounding flow and vice versa. This interaction is generally nonlinear making the modeling complicated. The mathematical analysis concentrates on the well-posedness of the models in order to provide a rigorous explanation of fundamental experiments. Various competing numerical approaches are discussed based on different variational formulations and mainly using finite element methods.
Mini-Workshop: Topology of closed one-forms and Cohomology Jumping Loci
The purpose of this workshop was to bring together researchers from the two different fields mentioned in the title, and to create more interaction and connections between these fields. Among the topics which appear in both subjects are Lusternik-Schnirelmann category, Bieri-Neumann-Strebel invariants and a spectral sequence introduced by Farber and Novikov.
Algebraic Groups
The workshop dealt with a broad range of topics from the structure theory and the representation theory of algebraic groups (in the widest sense). There was emphasis on the following areas: structure and classification of wonderful varieties, finite reductive groups and character sheaves, quantum cohomology of homogeneous varieties, representation categories and their connections to orbits and flag varieties.
Mini-Workshop: Category Theory and Related Fields: History and Prospects
he workshop concerned various topics in the history of category theory and related fields, paying attention to some extent also to open questions, present and possible future development.