bluuebunny/crossref_metadata_2025_split huggingface dataset:
Mathematical Biology
Authors: DiBenedetto Emmanuele , Perthame Benoît , Stevens Angela 
Published: December 2009

This meeting on Mathematical Biology tied in with the long tradition of these workshops in Oberwolfach and at the same time aimed to account for the fast growing synergy between biology and mathematics of the recent years. The use of new instrumentation and visualization methods at the molecular scale in biological and medical experiments allows for measurements which have not been possible a few years ago. Major questions for theoreticians and experimentalists are how to tackle this vast complexity of biological information and data, and, more important, if underlying principles can be found. Finding these would enable the field to become more predictive. Here is exactly where mathematical modeling, analysis, and simulation can contribute. On the other hand, mathematical biologists and mathematicians are now providing first new models to explain the measurements, and these models are ready for mathematical analysis.
The synergy between mathematics and physics, chemistry, engineering, and material sciences, has already proven to greatly advance the respective sciences and mathematics itself. To further deepen the connections between mathematics and biology, a group of experimental biologists, mathematical biologists, and mathematicians – especially many young scientists – met, joining the lively talks and discussions in this workshop.
The meeting intentionally focussed on some specific biological topics this time. Among those were cell movement, where results on the dynamics of the cellular cytoskeleton were presented, as well as on chemotaxis and cell adhesion. Questions of pattern and structure formation in cell systems were discussed for self-organizing microorganisms and cancer invasion. The analysis of structured population models in this context is new, but has a long tradition in ecology and epidemiology. Further topics of interest with clear mathematical challenges were transport and molecular motors, the organization of cell membranes, and the process of photo-transduction.
Wherever possible, the experimentalists talks were placed in tandem with related presentations on mathematical modeling.
Mathematical topics were: reaction-diffusion equations, parabolic and hyperbolic chemotaxis equations, fluid dynamics, variational principles and methods based on the Wasserstein distance, homogenization, singular perturbations, bifurcation analysis, and numerical simulations.
Besides the lectures, two discussion groups were organized, one on mathematical results for chemotaxis equations and one on cell motility. A round table discussion on ‘mathematical modeling in biology, aims and scopes’ rounded off the meeting, not to forget the nice concert, organized by some of the participants.
We would like to express our sincere thanks to the very dynamic and kind support of the Oberwolfach team before and during the workshop.
Applications of Asymptotic Analysis
Authors: Klein Rupert , Sanchez-Palencia Evariste , Sokolowski Jan , Wagner Barbara 
Published: December 2009

The workshop
Applications of Asymptotic Analysis
, organised by Rupert Klein (Potsdam), Evariste Sanchez-Palencia (Paris), Jan Sokolowski (Nancy) and Barbara Wagner (Berlin) was held June 18th–June 24th, 2006. This meeting was well attended with 46 participants with a broad geographic representation. This workshop was a nice blend of young and senior researchers with various mathematical backgrounds.

The objective of this workshop was to present the new developments of multiple scale asymptotics as they are developed for problems in various fields of application. It brought together experts working in different areas of asymptotic analysis and application fields and initiated exchange of new ideas and discussions of parallel developments.
On the whole the atmosphere of this workshop was very cheerful and characterized by the mutual interest into each others expertise and approach.
The themes of the workshop included:
Apart from these themes, various other lectures on applications of asymptotic analysis were given, ranging from applications in biology, solid mechanics to fluid mechanics, in particular thin liquid films.
Most of the lectures were given in the morning, with one hour overview lectures, followed by shorter half-hour talks. In the afternoon ample time was left for discussion sessions. Wherever possible the lectures and discussion sessions were grouped according to specific topics, which concerned the interplay of asymptotics and shape optimization (Monday), numerical analysis and asymptotics (Tuesday), mathematical theory and asymptotic methods (Wednesday, Thursday) and some new developments in homogenization theory (Friday).
Quadratic Forms and Linear Algebraic Groups
Authors: Hoffmann Detlev , Merkurjev Alexander , Tignol Jean-Pierre 
Published: December 2009

The workshop was organized by Detlev Hoffmann (Nottingham), Alexandr Merkurjev (Los Angeles), and Jean-Pierre Tignol (Louvain-la-Neuve), and was attended by 52 participants. Funding from the Marie Curie Programme of the European Union provided complementary travel support for young researchers, and it also allowed for the invitation of six PhD students in addition to established researchers.
The workshop followed a long and illustrious tradition of Oberwolfach meetings on quadratic forms initiated by M. Knebusch, A. Pfister and W. Scharlau in the 1970's. Initially, the topics ranged from the arithmetic theory of quadratic forms and lattices to real algebraic geometry. In the last decade, however, the algebraic theory of quadratic forms sustained a vigorous development of its own, under the influence of geometric methods, and new connections with linear algebraic groups over arbitrary fields appeared. Recently, striking new results, such as Voevodsky's proof of the Milnor conjecture, were obtained by an infusion of new techniques from motivic cohomology and algebraic topology.
The schedule of the meeting comprised 22 lectures of 45 minutes each, which presented recent progress and interesting new directions in various topics where the algebraic theory of quadratic forms, Galois cohomology, algebraic geometry and the theory of linear algebraic groups mutually stimulate each other, notably Witt groups of triangulated categories, Chow motives of homogeneous varieties, and the essential and canonical dimensions of algebraic groups. Some new connections with representation theory were also discussed.
Combinatorics, Probability and Computing
Authors: Alon Noga , Bollobás Béla , Wegener Ingo 
Published: December 2009

The conference was organized by Noga Alon (Tel Aviv), B\'ela Bollob\'as (Cambridge and Memphis) and Ingo Wegener (Dortmund). The programme consisted of 8 main lectures, supplemented by 21 shorter contributions, and covered many areas in Extremal and Probabilistic Combinatorics as well as in Theoretical Computer Science.
In its simplest form, the Probabilistic Method refers to the technique of proving the existence of structures with unexpected properties by showing that a randomly chosen object from an appropriate probability distribution has the properties with positive probability. The probabilistic method has been strikingly successful in Combinatorics, Graph Theory and Combinatorial Number Theory, and the probabilistic point of view has had an enormous influence on theoretical computer science.
The speakers reported on recent developments in Ramsey theory, including variants of these problems for Random Graphs and for Geometric questions, extending classical work in Functional Analysis. Extremal graph and hypergraph theory has also been discussed extensively, combining combinatorial, probabilistic and analytic tools. Additional active topics discussed included Percolation on quasi-random graphs and the properties of random triangulations of point sets in the plane as well as novel results in Complexity Theory including connections between communication complexity and geometric problems, and the study of refutation proofs for random instances of satisfiability.
The aim of the workshop was to focus on the connections and common themes of Combinatorics, Discrete Probability and Theoretical Computer Science. The diversity of the topics and participants stimulated a lot of fruitful discussions between researchers in different and yet related branches and gave rise to interesting discussions and new collaborations between the participants including the younger generation of researchers.
49 scientists, including 36 from countries other than Germany participated in the meeting. The organizers and participants would like to thank the Mathematisches Forschungsinstitut Oberwolfach for providing an inspiring setting for this conference.
Mathematical Theory of Water Waves
Authors: Craig Walter , Groves Mark D. , Schneider Guido 
Published: December 2009

The 1990s saw vigorous activity in the mathematical theory of water waves by several independent international research groups, and in response we organised a mini-workshop in Oberwolfach in 2001 entitled
Recent Developments in the Mathematical Theory of Water Waves.
The 2001 meeting, which was devoted to the exact equations for water waves as written down by Euler, was a great success. A collection of papers originating at the meeting were published in a special issue of the
Philosophical Transactions of the Royal Society
and lead to significant progress on certain famous and outstanding problems in water waves, particularly local existence and uniqueness, stability, three-dimensional waves, justification of model equations, convexity results for Stokes waves, and effective and accurate numerical schemes.

In view of the interest in water waves generated by the 2001 meeting and our subsequent endeavours, it appeared timely to bring the various research groups together in another Oberwolfach workshop to intensify research in this subject. The following topics were chosen as priority research areas for the workshop since
(i) they represent issues which have been almost fully settled for model equations, but remain almost fully open for the exact water-wave problem; and (ii) pose mathematical challenges whose resolution is likely to prove beneficial in a wide range of situations beyond the water-wave problem:
Significant new results in these areas were reported at the conference and are summarised in the extended abstracts below. The workshop was attended by twenty-three researchers from eight countries; there was a good mix of researchers who had attended the 2001 meeting and those who had not, and a number of younger researchers new to this field attended. Twenty 45-minute talks were held in a friendly and informal atmosphere and, in true Oberwolfach spirit, many collaborative discussions took place.
Mini-workshop: Statistical Methods for Inverse Problems
Authors: Hoffmann Marc , Reiß Markus 
Published: December 2009

The mini-workshop on “Statistical methods for inverse problems” gathered seventeen people from the area of statistics and numerical analysis. The goal of the workshop was to stimulate discussions around results and methods that are commonly used by different scientific communities. These methods mainly concern regularization of linear and nonlinear inverse problems in presence of deterministic or stochastic noise.
The week was articulated around three main lectures, divided into two talks each. Yuri Golubev (Université of Marseille) started on Monday–Tuesday mornings to give an extended lecture on inverse problems from a statistical perspective. He was quickly followed by Thorsten Hohage (University of Göttingen) who gave lectures on Monday–Tuesday afternoon on inverse problems from a numerical analysis perspective. A third lecture was given on Wednesday–Thursday morning by Rama Cont (École Polytechnique) who addressed the issue of inverse problems in finance, with both deterministic and probabilistic points of view. The main talks were completed by informal contributed talks of approximately one hour each, at the approximate rate of two talks per day except for the mandatory walk in the Schwarzwald, which was unfortunately canceled due to bad weather conditions that concentrated on the only day of rest!
Round tables were planned to follow the lectures, but the friendly and informal atmosphere soon raised constant questions and discussions among the participants during the lectures so that the workshop progressively moved to informal, yet intense scientific discussions: particular focus was given on optimal tuning parameter choice, stochastic or deterministic error modeling and the complexity of numerical schemes. These discussions took place during several extended talks that skipped the initially planned schedule, fortunately tightened by the strict meal hours of the Oberwolfach center.
The excellent atmosphere of the mini-workshop was made possible thanks to the exceptional working conditions at the MFO to which we would like to express our deep gratitude.
Mini-workshop: Dirac Operators in Differential and Noncommutative Geometry
Authors: Bär Christian , Sitarz Andrzej 
Published: December 2009

The mini-workshop, organized by Christian Bär and Andrzej Sitarz, had a very special character. The participating scientists came from two different mathematical communities: differential geometry (working mainly on problems related to the Dirac operator on spin manifolds) and noncommutative geometry (working mainly on concepts of Dirac operators in the framework of spectral geometry as postulated by Alain Connes).
Spin geometry has become an established and very active subfield of Differential Geometry, after Lichnerowicz observed that the Index Theorem yields a topological obstruction against the existence of metrics with positive scalar curvature. The Dirac operator plays a key role in the deep work of Gromov, Lawson, Rosenberg, Stolz and others on manifolds admitting metrics with positive scalar curvature.
The birth of noncommutative geometry offered completely new possibilities for extending some notions of differential geometry into the realm of operator algebras. In Connes' notion of spectral triples the Dirac operator was used to define a (possibly noncommutative) geometry itself rather than being an object derived from a geometry. Since then many interesting examples of noncommutative spaces and Dirac operators were studied. The equivalence theorem, allowing reconstruction of a spin manifold from a spectral geometry of a commutative algebra was proved only recently and the proof was presented at the workshop.
The aim of the workshop was twofold: to show current interests, methods and results within each group and open the possibility for interaction between two groups. Due to the character of the meeting, first three days were devoted to the expository presentations, when we tried to cover the possibly broadest scope of topics from one subject presented for the participants from the other group. The remaining two days were devoted to talks on advanced current research problems and results, which had closer links to the topics of both groups. During problem sessions in the evenings various open questions were discussed some of which were solved during the week.
Classical and Quantum Mechanical Models of Many-Particle Systems
Authors: Arnold Anton , Cercignani Carlo , Desvillettes Laurent 
Published: December 2009

The Oberwolfach meeting described here aimed at presenting the latest mathematical results in the field of kinetic theory (both classical and quantum).
There were 50 participants, among which 15 young participants (PhD students, post-docs or young assistant professors). Two of them (M.-P. Gualdani and R. Strain) were invited within the program “US Junior Oberwolfach Fellows”: they are promising young researchers working in the US.
The program of the meeting was made in such a way that a lot of time remained for people to meet informally and discuss about scientific issues. It also ensured that almost everybody attended all (or most of) the scheduled talks .
The program was structured in the following way: three subtopics were defined (relationships between micro/meso/macroscopic models; kinetic theory for complex particles: granular media, coagulation/fragmentation, chemotaxis and sprays; quantum mechanical kinetic theory). For each subtopic, there were a few (2 or 3) longer talks (about 40 minutes) by senior participants. For those talks, a specific effort of clarity was asked to the speakers, and the subject had to be rather broad.
Then, shorter talks of about 20 minutes were planned , on more specialized issues. Finally, a special (much longer) talk in two parts was presented by one of the participants (C. Villani), in order to describe in a very didactical way an emerging link between kinetic theory, optimal transport, and Riemannian geometry.
Some participants did not give a talk within this program, but organized an informal discussion around a poster, with an audience composed of specially interested people.
Here is a brief description of each of the subtopics.
We finally would like to emphasize the ideas and trends which have emerged within the two or three last years and which have been present in this Oberwolfach meeting: a new approach of the relations between the hydrodynamic and non hydrodynamic part of the Boltzmann equation; explicit estimates for the spectrum of the linearized Boltzmann equation when the kernel is singular; the treatment of coagulation/fragmentation equations as infinite-dimensional reaction-diffusion equations with the help of entropy methods; the use of the ideas of kinetic theory in fields coming out from the industry rather than from theoretical physics (supply chains, industrial sprays, etc.).
Mini-Workshop: Lévy Processes and Related Topics in Modelling
Authors: Barndorff-Nielsen Ole E. , Jacod Jean , Klüppelberg Claudia 
Published: December 2009

The theory of infinite divisibility, Lévy processes and Lévy bases and its applications is an area of very active current interest. This trend is of relatively new origin, dating back around 10 years. In this period larger research conferences on “Lévy Processes and their Applications” have been held on a regular basis, about every 2 years and at different locations around Europe. In addition intermingled between these conferecnes there has been a number of more specialized workshops within the area. One of these was organized at the Isaac Newton Institute, Cambridge, 2 1/2 years ago, the organizers being Professor Neil Shephard and Ole E. Barndorff-Nielsen, on invitation by the Newton Institute. The format of that workshop where the focus was on new ideas and ongoing research, rather than on finished work, and where the presentations were rather short, in some cases even down to about 15 minutes, was found to be very stimulating and productive. The same format was largely followed at the Mini-Workshop under reporting here and was found again to be very productive. Although the workshop was somewhat specialized a rather wide range of topics were treated in the presentations and in informal discussion groups.
Half of the participants were junior researchers, visiting the MFO for the first, or in some cases the second, time. Like the more senior people they were delighted by the warm atmosphere and excellent conditions for research provided by the Institute. And by lucky coincidence, due to the weather the traditional midweek afternoon excursion was shifted to the Thursday afternoon which was the first day of the Fastnacht celebrations in Oberwolfach with the parade of the “coffee aunts”. This made for a rather unique and refreshing break in the otherwise intense programme.
The first talk of the workshop, by Philip Protter, presented an overview of issues in mathematical finance. The talks by Fred Espen Benth, Jean Jacod, Thilo Meyer-Brandis, Mark Podolskij, Robert Stelzer, and Viktor Todorov discussed modelling and inference on volatility and jumps for financial dynamics. A variety of theoretical results on Lévy processes were presented in talks by Søren Asmussen, Friedrich Hubalek, Andreas Kyprianou, Alexander Lindner and Tina Marquardt, while other talks, by Makoto Maejima, Víctor Pérez-Abreu, Jan Rosiński and Steen Thorbjørnsen concerned work on new aspects of infinite divisibility. Finally, the talk by Anna Amirdjanova treated problems in the theory of Gaussian processes.
Analysis and Numerics for Rate-Independent Processes
Authors: Dal Maso Gianni , Francfort Gilles A. , Mielke Alexander , Roubíček Tomáš 
Published: December 2009

This conference brought together the mathematicians and engineers concerned with the study of rate-independent processes. The topics involved the physical and mechanical modeling, the analytical treatment as well as the development of numerical algorithms and the computational aspects.
Rate-independent processes occur when a system undergoes loadings varying on a time scale much slower than the internal relaxation times of the system. However, the system still stays in metastable states and does not find its thermodynamical equilibrium because of internal frictional processes. There are many well-established macroscopic theories, which show good agreement with experiments, for instance the classical theory of linearized elastoplasticity. This theory has been established a century ago, but its mathematical foundations were only understood 30 years ago using the theory of convex analysis and variational inequalities. Another classical driving theme in this area is the theory of Coulomb friction between rigid or elastic bodies.
Within the last decade similar models have been developed in several areas of mechanics of solids, some of them on a phenomenological basis and others relying on an improved understanding of the microstructures. Such areas include multifunctional or active materials (e.g., shape-memory alloys, ferromagnetism, magneto- and electro-strictivity) and inelastic processes in solids (e.g., elastoplasticity, damage, delamination, fatigue, brittle fracture, crack growth).
Although many of these models are used in engineering, their mathematical understanding is insufficient and efficient numerical algorithms for the computation of approximate solutions are few. The main problem is the inherent nonsmoothness of the modeling because of rate independence.
We discussed a new approach based on an energetic formulation, which provides a broad basis for treating quite general models using topological, geometrical and measure theoretical methods that do not require a Banach space structure. It was shown in various presentations that this approach allows one to go beyond linearized elastoplasticity and to treat fully nonlinear mechanical problems, like crack formation and growth, or elastoplasticity with softening.
Finally, the modeling of the formation and evolution of microstructures was debated in several talks and gave rise to a better understanding of the physical and mathematical underlying principles.
The specific methods discussed were:
The specific applications discussed were:
The continuous downpour of Black Forest Rain created a cosy atmosphere that fostered the interaction between the different mathematical and engineering communities.