bluuebunny/crossref_metadata_2025_split huggingface dataset:
Mini-Workshop: Shape Analysis for Eigenvalues
Authors: Bucur Dorin , Buttazzo Giuseppe , Henrot Antoine 
Published: December 2009

The mini workshop
Shape analysis for eigenvalues
, organised by Dorin Bucur (Chambéry), Giuseppe Buttazzo (Pisa) and Antoine Henrot (Nancy) was held April 8th–April 14th, 2007. This meeting was attended by 18 participants.

The question of localizing or optimizing the eigenvalues differential operators has applications in several domains like acoustics, quantum mechanics, visualization, solid or fluid mechanics and bio-mathematics. Those questions have also a specific mathematical interest since they melt geometrical questions with analysis of partial differential equations and provide model problems for general and applied shape optimization problems.

Despite (or because) their false simplicity, several problems are still open, although formulated hundreds year ago (see for instance the recent books by Bucur & Buttazzo
Variational Methods in Shape Optimization Problems
, Birkhäuser-Verlag, 2005 and Henrot
Extremum problems for eigenvalues of elliptic operators
, Birkhäuser, 2006) and give rise to important debates within the international scientific community. Among them, we can cite

Each of these problems is associated to one or several constraints for the geometries, which may be local or not local (convexity, connectedness).
One of the goals of the proposed mini-workshop was to bring together two mathematical communities working on the topics above by quite different methods. On the one hand explicit solutions to optimal shape problems for eigenvalues are searched by means of direct estimations, symmetrizations, rearrangements; on the other hand recent techniques of variational type have been developed to prove the existence of an optimal shape and intensive research is carried out to prove the regularity of the free boundary and to analyze the optimality conditions.
A second main issue was to present the state of the art on some famous open problems and conjectures, and try to make a step forward in the direction of solving them.
The organization of the mini-workshop was the following: mornings were devoted to lectures by participants while each afternoon began by an open problems session and smaller working groups (4-5 persons) were organized to work on these problems.
Non-Classical Interacting Random Walks
Authors: Comets Francis M. , Zerner Martin 
Published: December 2009

The workshop was organized by Francis Comets (Paris 7) and Martin Zerner (Tübingen). It was attended by fifty participants of about twenty different nationalities. Among the participants was a relatively large number of young researchers, some of which were supported by the European Union within the Marie Curie Conferences Programme and by the National Science Foundation.

The title of the workshop was
Non-Classical Interacting Random Walks
. The study of random walks (RWs) goes back to the beginnings of probability theory in the seventeenth century. Some of the first probabilists like Bernoulli and Pascal investigated the properties of coin tossing sequences and other simple games of chance, which nowadays are modeled by RWs. Such a RW takes steps at fixed time intervals, and at each step a random direction is chosen, which gives a chaotic trajectory. So in their most stringent definition, RWs come up as sums of independent and identically distributed random variables with real or often integer lattice values. A somewhat wider definition includes time-homogeneous Markov chains whose transition probabilities are in some way adapted to a given geometric-algebraic-combinatorial structure of the underlying state space. In this context, many tools from potential theory, graph theory, harmonic analysis and Fourier analysis are available.

The focus of this workshop was on a quite different area of current research on RWs. This is what the term “non-classical” in the title refers to. Some of the RWs, which are currently heavily investigated, are quite “irregular”: Some are not Markovian, but are influenced by their own past. Others are Markovian, but interact with a possibly random environment, which influences the transitions of the walk. Many of the tools used in the more traditional settings of RWs fail in this context.
The main models considered in this workshop were RWs in random environments (RWRE) with talks mainly on Monday, RWs in random potential and random polymers on Tuesday, excited RWs on Wednesday morning, followed by an exciting open problem session in the evening, reinforced RWs on Thursday and various other RWs on Friday. The programme consisted in total of 23 talks of about 50 minutes each and the open problem session. On most days a long lunch break from 12:30 to 16:00 gave plenty of opportunity for interaction between the participants. Following the reinforcement by previous workshops and in spite of the title of the current workshop, on Wednesday afternoon most participants took part in the classical interacting non-random walk to St. Roman.
Adaptive Numerical Methods for PDEs
Authors: Rannacher Rolf , Süli Endre , Verfürth Rüdiger 
Published: December 2009

Multidimensional processes in sciences and engineering are usually formulated in terms of partial differential equations. With the incorporation of more and more complete physics these models become increasingly complex. Their accurate numerical simulation requires the use of efficient methods which exploit concepts of adaptivity in setting up the models and their discretization. Over the last two decades these approaches have been developed from simple model situations towards real-life applications, in most cases with striking success. The conference “Adaptive Numerical Methods for PDEs” had its focus on basic questions related to the rigorous mathematical understanding of these methods and to their practical use.

The use of automatic adaptivity has become common in the simulation of all kind of PDE models even in situations where a solid theoretical justification is lacking. Examples are the nonlinear Navier-Stokes equations in fluid mechanics, the nonlinear Lamé–Navier equations in large-strain elasticity, the Maxwell equations, and combinations of these models in nonstationary fluid-structure interaction and magneto-hydrodynamics. Such approaches are usually based on
a posteriori
information in terms of local quantities such as approximate gradients or residuals obtained from the computed solution. The extension of quantitative mathematical analysis of adaptive methods to such complicated models is a challenging problem.

The existing methods of a posteriori error estimation and mesh adaptation are based on several heuristic technical assumptions. These are assumptions about the convergence of higher-order difference quotients, the relative “smallness” of linearization errors, “sharpnes” of stopping criteria of algebraic iterations, the “safe” control of error accumulation in long-time calculations, etc. These aspects are fundamental to adaptive methods and still need rigorous mathematical analysis for a better understanding of the underlying mechanisms.
Recently, several new directions of adaptivity have evolved, e.g., “spectral-adaptivity” in wavelet analysis, “hp-adaptivity” in high-order FE-methods, “anisotropic” refinement in the approximation of layers, adaptivity in the solution of “optimal control” problems, “model adaptivity” for example in spatial dimension reduction or the complexity reduction in diffusion models, and “multi-scale” adaptivity in problems with micro- and macro-scales reaching even towards adaptive turbulence modeling. The latter are the really “hot” topics in current Numerical Analysis research. The mathematical analysis of these approaches has to combine concepts of a posteriori error estimation with techniques from PDE theory. The talks given at this conference were concerned with the following subjects:
Differentialgeometrie im Grossen
Authors: Biquard Olivier , Kleiner Bruce , Leeb Bernhard , Tian Gang 
Published: December 2009

The meeting continued the biannual conference series
Differentialgeometrie im Großen
at the MFO which was established in the 60's by Klingenberg and Chern. Traditionally, the conference series covers a wide scope of different aspects of global differential geometry and its connections with topology, geometric group theory and geometric analysis. The Riemannian aspect is emphasized, but the interactions with the developments in complex geometry, symplectic/contact geometry/topology and mathematical physics play also an important role. Within this spectrum each particular conference gives special attention to two or three topics of particular current relevance.

The scientific program consisted of 22 (almost) one hour talks leaving ample time for informal discussions.

This time, a main focus of the workshop were
geometric evolution equations
. 6 talks discussed the Ricci flow and its applications to the geometrization of 3-manifolds, the Ricci flow in arbitrary dimension and applications to Riemannian manifolds of positive curvature, the Kähler–Ricci flow and the (inverse) mean curvature flow.

A second focus was the
geometry of singular spaces
(5 talks), that is, metric spaces with sectional curvature bounds (in the sense of Aleksandrov), Gromov-hyperbolic spaces and Carnot spaces with connections to geometric group theory. One of the talks discussed the theory of collapse with lower curvature bound which is another ingredient (independent of Ricci flow) in the argument for geometrization in dimension

3

.

Other talks covered results about
geometric structures on manifolds
(hyperbolic geometry and representation varieties), from
geometric analysis
(Dirac operators, metrics of positive scalar curvature),
symplectic and contact geometry
(open book decompositions, confoliations, construction of special Lagrangian submanifolds with isolated conical singularities), and
complex geometry
(extremal metrics on Kähler manifolds, Kähler–Ricci flow).

There were 52 participants from 8 countries, more specifically, 23 participants from Germany, 12 from France, 6 from other European countries, and 11 from North-America. 6 were young researchers (less than 10 years after diploma or B.A.), both on doctoral and postdoctoral level. The organizers would like to thank the institute staff for their great hospitality and support before and during the conference.
The financial support of the European Union (in particular for young participants) is gratefully acknowledged.
Mini-Workshop: The Reception of the Work of Leonhard Euler (1707-1783)
Authors: Grattan-Guinness Ivor , Pulte Helmut 
Published: December 2009

Quite a number of scholars work on all aspects of Euler, especially in connection with the continuing preparation of the edition of his Opera omnia. But the historical study of the reception of his work during his lifetime and especially after his death has been rather patchy; for example, in the general volume [1] to commemorate the bicentenary of his death and in the recent Euler handbook [2] to note the tercentenary of his birth few articles dealt with aspects of reception in any depth. (This point holds of reception history in general.)
In our workshop the reception of Euler's work was usually considered up to around 1840. After that, it seems that it was ordinarily either used routinely or replaced, or quite forgotten, or was studied historically; a few exceptions are noted.
Sixteen scholars came together from eight countries to present their ideas on Euler's influence in a number of mathematical areas. The selection of topics is indicated in the table of contents; it includes several from applied mathematics, where scholarship is especially limited. We also discussed some examples of Euler's influence in various countries, but this kind of history is even less well developed than the influence by areas! In addition, we aired other neglected historical questions, such as: why was there such a small reception of the many papers and other writings that were posthumously published by the Saint Petersburg Academy between 1783 and 1862?

The sign ‘E

n

’ in the abstracts below indicates the number

n

of an Euler writing according to the list that was prepared in the early 1910s by the historian Gustav Eneström.

The meeting was a success and we are thinking of building up our efforts into a book on Euler's influence.
Komplexe Algebraische Geometrie
Authors: Catanese Fabrizio , Kawamata Yujiro , Tian Gang , Viehweg Eckart 
Published: December 2009

The Workshop
Komplexe algebraische Geometrie
, organized by Fabrizio Catanese (Bayreuth), Yujiro Kawamata (Tokyo), Gang Tian (Princeton), and Eckart Viehweg (Essen), drew together 50 participants. There were several young PhD students and other PostDocs in their 20's and early 30's, together with established leaders of the fields related to the thematic title of the workshop. There were 23 talks, each lasting 55 minutes or one hour, and each followed by a lively 10 minutes discussion.

As usual at an Oberwolfach Meeting, the mathematical discussions continued outside the lecture room throughout the day and the night. The Conference fully fulfilled its purported aim, of setting in contact mathematicians with different specializations and non uniform background, of presenting new fashionable topics alongside with new insights on long standing classical open problems, and also cross-fertilizations with other research topics as arithmetic and physics. For the latter, cf. the talk by Bernd Siebert on the new approach to Mirror Symmetry through logarithmic geometry and toric affine Calabi Yau varieties and the one by van Straten on quantization of completely integrable Hamiltonian Systems. For the former, cf. the talks by Winkelmann on integral sets and by McQuillan on the Bloch principle.
A central role was occupied by the new results around the Hodge conjecture presented by Voisin, and the new results by Hacon, McKernan et al which give an essential step towards the final solution of the Minimal Model Program, and were presented here by McKernan with a proposed approach to the Sarkisov program.
There were many expositions dealing with several classical problems and classical and modern theories. It would take too long to dwell on each of the outstanding contributions presented at the Conference. For some topics there were several interrelated talks, for instance we could mention the following classical themes:
There were also expositions on many other beautiful topics:
The variety of striking results and the very interesting and challenging proposals made the participation in the workshop rather strenuous but certainly highly rewarding. We hope that the quality of the expositions in these abstracts will make them quite useful to the mathematical community.
Harmonische Analysis und Darstellungstheorie Topologischer Gruppen
Authors: Kobayashi Toshiyuki , Krötz Bernhard , Lapid Erez , Torossian Charles 
Published: December 2009

This international conference was organized by Toshiyuki Kobayashi (University of Tokyo), Bernhard Krötz (MPIM Bonn), Erez Lapid (Hebrew University) and Charles Torossian (Paris VI). The general theme was representation theory of real and p-adic Lie groups, especially in connection to automorphic forms. In addition there were very interesting presentations on infinite dimensional Lie groups and quantization.
It was very pleasing that new results of the highest caliber were presented by the youngest of the participants. There were many discussions at this relaxed and influential meeting. We would like to thank the MFO for having given us this wonderful opportunity. The organizers would like to thank Dmitry Gourevitch for his careful work in compiling and editing this report.
Mini-Workshop: Arithmetik von Gruppenringen
Authors: Jespers Eric , Marciniak Zbigniew , Nebe Gabriele , Kimmerle Wolfgang 
Published: December 2009

The mini workshop "Arithmetic of group rings" was attended by 16 participants from Belgium, Brazil, Canada, Germany, Hungary, Israel, Italy, Romania and Spain. The expertise was a good mixture between senior and young researchers. It was a very stimulating experience and thesize of the group allowed excellent discussions amongst all participants. Very fruitful were the problem sessions, resulting in the problems listed at the end of this report.
The main highlights of the conference were:
The complete calculation of the projective Schur subgroup of the Brauer group by Aljadeff and del Rio.
Hertweck's solution of the first Zassenhaus conjecture for finite metacyclic groups.
the description of special subgroups of the unit group of integral group rings, such as the hypercentre and the finite conjugacy centre, and the relation with respect to the normalizer of the trivial units.
discussion of the present state of art via several survey talks presented and the problem sessions

The group

G

determines its integral group ring

\mathbb Z G

and its group

V(\mathbb Z G)

of normalized units. Several talks addressed the interplay of the cohomological properties of these three objects. Further topics included twisted group rings, group rings over local rings, polynomial growth and identities, orders and semigroup rings, Lie structure, representation-theoretic and algorithmic methods.
Set Theory
Authors: Friedman Sy-David , Magidor Menachem , Woodin W. Hugh 
Published: December 2009

This was a highly successful workshop on some of the exciting recent developments in set theory. There were 45 participants. By limiting the number of talks to 25, there was ample time for research collaboration in small groups, which rendered the meeting very relaxed, enjoyable and productive.
Among the highlights of the workshop are the following:
Justin Moore presented some dramatic new work on the existence of a universal Aronszajn line, demonstrating that the existence of a canonical, universal linear ordering is not limited to the countable case. There were several beautiful presentations in the area of descriptive set theory: Christian Rosendal provided a rough classification of Banach spaces, Slawomir Solecki described G-delta ideals of compact sets, Simon Thomas drew some striking connections between set theory and geometric group theory and John Clemens discussed Borel homomorphisms of smooth Sigma-ideals. A major new result was presented by David Schrittesser, who showed that projective measurability does not imply the projective Baire property.
There were two major results in the related areas of large cardinals and determinacy: John Steel calculated the consistency strength of determinacy for games on reals and he together with Ronald Jensen discovered a way of building the core model for a Woodin cardinal in ZFC without additional large cardinal hypotheses. Several talks presented important recent work related to the pcf theory: Todd Eisworth discussed combinatorial properties at the successor of a singular cardinal, Matteo Viale told us about reflection and approachability and Moti Gitik brought us up to date on consistency results regarding the behaviour of the generalised continuum function.
In combinatorial set theory we heard lectures on induced Ramsey theory, MAD families, weak diamonds and simple cardinal invariants. And in the theory of forcing we heard about Laver products, p-points, indestructibility of weak compactness, mixed support iterations and reflection.
Paul Larson's very nice talk on Martin's Maximum and definability rounded out a very successful meeting.
Mini-Workshop: Mathematics of Solvency
Authors: Delbaen Freddy , Eisele Karl-Theodor , Hipp Christian 
Published: December 2009

The mini-workshop
Mathematics of Solvency
, organised by Freddy Delbaen (Zurich), Karl-Theodor Eisele (Strasbourg) and Christian Hipp (Karlsruhe) was held during the week February 10th–February 16th, 2008. The 15 participants from academia and practice – most of whom came from supervision authorities – discussed the foundation of mathematical concepts for risk and risk measurement as well as their consequences for various decision or control activities in financial services. Such concepts are of major importance for the definition of a necessary solvency capital – which takes into account diversification effects – for banks, investors, and insurers, from the perspective of supervision, of risk management, of rating, and of capital allocation. They help industry to develop consistent foundations for dealing with insurance and financial risks.

The investigation of risk concepts in the multi period setting leads to new mathematical questions in the theory of stochastic processes. A sensible definition of a risk measure requires the property of super-additivity with respect to different risks as well as a submartingale property with respect to time. Such a definition leads to a theory of non-linear pricing of risks, as well as to a better understanding of the time evolution of risk assessment. These two concepts were not treated in traditional finance.
The consistency of risk measurement over different time intervals leads to monotonicity properties of convex functionals. The representation of these time consistent valuations is related to backward stochastic differential equations and difference equations, respectively. The information available to agents is modeled with filtrations and the difference in information leads to problems known as enlargement of filtrations.
In the talks, methods and concepts from various fields were used: stochastic processes, game theory, functional analysis, and stochastic control. In addition, experience with existing and operating real world risk valuation concepts has been reported and discussed.