bluuebunny/crossref_metadata_2025_split huggingface dataset:
Algebraic Groups
Authors: Brion Michel , Jantzen Jens Carsten , Rouquier Raphaël 
Published: December 2009

The workshop continued a series of Oberwolfach meetings on algebraic groups, started in 1971 by Tonny Springer and Jacques Tits who both attended the present conference. This time, the organizers were Michel Brion, Jens Carsten Jantzen, and Raphaël Rouquier.
During the last years, the subject of algebraic groups (in a broad sense) has seen important developments in several directions, also related to representation theory and algebraic geometry. The workshop aimed at presenting some of these developments in order to make them accessible to a “general audience” of algebraic group-theorists, and to stimulate contacts between participants.
Each of the first four days was dedicated to one area of research that has recently seen decisive progress:
The first three days started with survey talks that will help to make the subject accessible to the next generation. The talks on the last day introduced to several recent advances in different areas: arithmetic groups, eigenvalue problems, counting orbits over finite fields, quivers and reflection functors. In order to leave enough time for fruitful discussions, the number of talks (generally of one hour) was limited to four per day.
Besides the scientific program, the participants enjoyed a piano recital on Thursday evening, by Harry Tamvakis.
The workshop was attended by 53 participants, coming mainly from Europe and North America. This includes 6 PhD students, supported by the Marie Curie program of the European Union. The organizers are grateful to the EU for this support, and to the MFO for providing excellent working conditions.
Arithmetic and Differential Galois Groups
Authors: Harbater David , Matzat B. Heinrich , van der Put Marius , Schneps Leila 
Published: December 2009

Galois theory is the study of symmetries in solution spaces of polynomial and differential equations and more generally of the relation between automorphism groups (or group schemes) and the structure of algebraic and differential extensions.
Many of the important problems in this area are connected to the classification of (algebraic or differential) Galois extensions and the study of the respective fundamental groups, e.g. via inverse problems. Other interesting points are the direct problem, i.e., the computation of (ordinary or differential) Galois groups, and related constructive aspects.
This workshop gave an overview on some important new results and developments. A second goal was the discussion of ideas for proving some open questions and conjectures as well as of new directions of research.
The main topics of the workshop were:
Besides this main program we had some reports on related subjects like the Cohen-Lenstra heuristics for number fields by J. Klüners and the behaviour of the Tate–Shafarevich group in anticyclotomic field extensions by M. Çiperiani.

It is always difficult to emphasise highlights or unexpected results, but one of them might be the result of F. Pop that henselian fields always are large, which is of great interest in field arithmetic and inverse Galois theory. Another striking result is the existence of

G_2

-motives over

\mathbb{Q}

shown by M. Dettweiler which gives a positive answer to an old question of J.-P. Serre. A fruit of common effort in research in arithmetic and differential Galois theory is the development of patching methods for differential modules by D. Harbater and J. Hartmann. This method will allow yet unexpected applications in inverse differential Galois theory and other areas, like K-theory. The talk of B. Malgrange gave a vision of Galois theory for nonlinear differential equations. Exploitation of his work for special types of equations, like Painlevé equations, and the generalization of his ideas to non algebraically closed fields of constants as well as to positive characteristic will keep researchers busy for years.

Surely, many other results presented at the workshop should be pointed out here, too, like M. Raynaud's work on fundamental groups in positive characteristic, D. Bertrand's result on Schanuel's conjecture or Ch. Hardouin's generalization of

q

-difference equations to roots of unity by creating an iterative

q

-difference theory.

Altogether, we had a wonderful and inspiring week with lots of interesting lectures and many discussions bearing ideas for future research.
Finally, the organisers want to cordially thank the Oberwolfach administration and its staff for giving us the opportunity to arrange this and earlier workshops on Galois theory as well as for the excellent service.
Partielle Differentialgleichungen
Authors: Ilmanen Thomas , Schätzle Reiner , Trudinger Neil S. 
Published: December 2009

The workshop
differential equations
, organised by Tom Ilmanen (ETH Zürich), Reiner Schätzle (Universität Tübingen) and Neil Trudinger (Australian National University Canberra) was held July 22–28, 2007. This meeting was well attended by 50 participants, including 6 females, with broad geographic reprensentation. The program consisted of 19 talks and 3 shorter contributions and left sufficient time for discussions.

One focus was the combination of nonlinear partial differential equations and geometric problems. There were talks on monotonicity formulas in presence of degenerate singularities and on estimates of the singular set for branched minimal immersions. One striking new result was the proof of the diffeomorphic sphere theorem by the use of Ricci flow.
Many leading experts in the regularity of elliptic and variational problems and in fully nonlinear differential equations occuring in optimal transport and in Hessian equations attended the workshop. Several main contributions were given to this subject. Here, we mention the proof of interior estimates for quadratic Hessian equations in three dimensions, which has been an open problem for several years of similar relevance as the gradient estimates for the minimal surface equation.
New results were also presented for the Willmore functional. It was achieved to write the Euler-Lagrange equation in divergence form, and the existence of minimizers in fixed conformal classes with certain energy bounds were obtained.
The organisers and the participants are grateful to the Oberwolfach Institute for presenting the opportunity and the resources to arrange this interesting meeting.
Mini-Workshop: Topology of closed one-forms and Cohomology Jumping Loci
Authors: Farber Michael , Suciu Alexander I. , Yuzvinsky Sergey 
Published: December 2009

This Mini-Workshop was organized by M. Farber (Durham), A. Suciu (Boston) and S. Yuzvinsky (Eugene). It brought together researchers working on two distinct, yet related topics:
Even though these two fields share some common roots, so far they have developed in parallel, with not much overlap or interaction. Nevertheless, it is becoming increasingly apparent that there are deep connections between the two theories, with potentially fruitful applications going both ways:
Given the multifaceted nature of these topics, the meeting brought together people with a variety of backgrounds, including topology, algebra, discrete geometry, geometric analysis, and singularity theory. Several participants were recent Ph.D.'s, most of them on their first visit to Oberwolfach. In all, there were 16 people attending the workshop (including the organizers), coming from the United States, Great Britain, France, Romania, Canada, and Germany.
The Mini-Workshop provided a lively forum for discussing a host of questions related to the themes listed above. The day-by-day schedule was kept flexible, and was agreed upon on short notice, making it possible to shape the program on-site, and in response to the interests expressed by the participants. The borderline between problem sessions and formal lectures were often blurred. Spending a concentrated and highly intense week in a relatively small group allowed for in-depth and continuing conversations, in particular with new acquaintances. These opportunities were enhanced by the diversity of backgrounds of the participants.
A basic objective of the Mini-Workshop was to bring together some of the people most actively working in two related fields, and to seek common ground for further advances and collaborations. In the ideally suited research atmosphere at Oberwolfach, participants had the opportunity to explain their respective approaches, and the variety of techniques they use. The lively atmosphere and the free-flow of ideas led to a deeper understanding of the subject, to progress in solving several open problems, and to fruitful insights on how to attack new problems.
Nonlinear Waves and Dispersive Equations
Authors: Kenig Carlos E. , Koch Herbert , Tataru Daniel 
Published: December 2009

Dispersive equations occur as asymptotic models for the propagation of linear and nonlinear waves. Mathematically they display an interplay between linear dispersion and nonlinear focusing and defocusing effects. They are linked to diverse areas of mathematics and physics, ranging from nonlinear optics over oscillatory integrals to integrable systems. The workshop focused on a PDE based approach to dispersive equations.
Current activities covered by the workshop include:
There is a large number of promising young mathematicians working in this area. The meeting was attented by 45 participants. The organizers gave a strong preference to talks by young researchers.
Coagulation and Fragmentation Models
Authors: Bertoin Jean , Norris James R. , Wagner Wolfgang 
Published: December 2009

Historically deterministic equations were used for modelling the dynamics of the density of clusters of different sizes in a medium that evolves by coagulation and/or fragmentation. An alternative stochastic approach uses the distribution of a typical particle in systems undergoing a random evolution. This approach provides tools for deriving limit equations, it easily extends to more general interactions and, finally, it shares the familiar advantages of particle-based methods for computing distributions in high dimensions. The stochastic theory is undergoing intense development, both at a theoretical level, in the construction of models and analysis of their properties, and at a computational level. Major mathematical challenges in the field of coagulation and fragmentation models are related to phase transitions due to fast coagulation (gelation) or fast fragmentation (formation of dust), and to explicit descriptions of the structure of partitions (e.g. allelic partitions induced by random mutations in models for the evolution of populations). A further direction of intensive study is the detailed analysis of particular coagulation and fragmentation processes, where special features (e.g., scaling properties) allow links to be made to Brownian motion and other Lévy processes, also to some interesting problems in random combinatorics.
Major topics that have been discussed during the workshop include :

1. Spatial models of coagulation and fragmentation
Models incorporating diffusion; scaling limits; derivation from particle dynamics; equilibrium measures for coagulation-fragmentation processes; formation of structured particles; diffusion limited aggregation

2. Phase transitions in coagulation and fragmentation models
Gelation effects; shattering transition (appearance of dust in fragmentation); explosion phenomena; computation of the gelation time; uniqueness issues; convergence of particle systems

3. Aspects of random combinatorics

Links to random graphs and trees; genealogy for certain large populations dynamics; mutation and allelic partitions; stochastic coalescents with multiple collisions (

\Lambda

-coalescents) and fragmentations

4. Computational issues
Approximation and numerics; analysis of algorithms; Monte Carlo issues around sensitivity in initial conditions and kernel parameters
Combinatorics
Authors: Kahn Jeff , Lovász László , Prömel Hans Jürgen 
Published: December 2009

The workshop
Combinatorics
organised by Jeff Kahn (Piscataway), László Lovász (Budapest), and Hans Jürgen Prömel (Berlin) was held January 6st–January 12th, 2008. This meeting was very well attended with 46 participants from many different countries. The programme consisted of 15 plenary lectures, accompanied by 18 shorter contributions and a vivid problem session led by Vera T. Sós.

The conference is a workshop on Combinatorics in a very broad sense, and is in part intended to serve as a framework for all other Oberwolfach meetings that focus on particular areas within combinatorics. This meeting over the years has been extremely successful in achieving the sometimes elusive goal of bringing together and fostering interactions among people with a wide range of interests, and we feel that the program this time was close to ideal in its coverage of a large fraction of the most exciting recent developments across the combinatorial spectrum. Quite a few of the talks – for instance those of Chudnovsky, Kühn, Osthus, Ruciński, Sudakov, Taraz and Vu – reported major progress on well-known problems. Some of the plenary speakers were asked to give overviews of areas somewhat distant from the central interests of many of the participants.
The breadth of the conference makes its contents nearly impossible to summarize. One might say that the central foci of the meeting were extremal and probabilistic aspects of combinatorics, and graph theory; but “extremal combinatorics” is an extremely broad term, and a glance at the titles below shows that the list of topics is not much shorter than the list of talks. Thus, even among the talks that could be considered to fall in the above categories, one finds geometry, Fourier analysis, algebra, physics, connections with social sciences, and multiple connections with computer science and related technology.
Again, we consider this breadth to be not a drawback, but a central feature of the meeting. It has promoted an inspiring, interactive atmosphere, and led to fruitful discussions and collaborations, to new awareness of what's happening in different parts of combinatorics, and to the discovery of some unexpected connections.
More than in past meetings, an emphasis was placed on talks (both plenary and shorter) by younger researchers. This too worked very well, and we hope to make it the pattern for future meetings.

On behalf of all participants, the organisers would like to thank the staff and the director of the
Mathematisches Forschungsinstitut Oberwolfach
for providing a stimulating and inspiring atmosphere.
Optimal Control of Coupled Systems of PDE
Authors: Kunisch Karl , Leugering Günter , Sprekels Jürgen , Tröltzsch Fredi 
Published: December 2009

The international conference
Optimal Control of Coupled Systems of PDE
, was held March 2nd–March 8th, 2008, organized by K. Kunisch (Karl-Franzens-University Graz), G. Leugering (University of Erlangen-Nürnberg), J. Sprekels (Weierstrass Institute of Applied Analysis and Stochastics Berlin) and Fredi Tröltzsch (Technische Universität Berlin). 44 participants attended this meeting and followed 33 talks on optimal control and related topics.

Mathematically, the control of partial differential equations (PDEs) is concerned with the following type of problems: The solution of a PDE (the state of the system) should be influenced in a desired way by the choice of certain control functions or control parameters (the controls), which may occur in different terms of the differential equation. If the controls are to minimize a certain functional related to the state, then an
optimal control problem
is posed. If the domain underlying the PDE is subject of the control, then a
shape optimization problem
is given. For evolution equations, it can be required to move the solution from a given initial state exactly to a desired final state. This is the question of exact
controllability
.

Optimization and control of partial differential equations continues to be a very active field of research. Scientists working in different fields came together to report on their contributions to the numerical analysis of control problems. It is remarkable that optimal control is a challenge for researchers with backgrounds in related fields such as the theory of systems of nonlinear PDEs, numerical methods for solving them, large scale nonlinear optimization, or the numerical simulation and optimization of complex processes in engineering or medical science.
This diversity was reflected by the conference program. Talks were focused on
All these issues are currently subject of active research. In extensive and lively discussions, the participants of the workshop produced new mathematical ideas and tightened connections of joint cooperation.
Random Schrödinger Operators and Random Matrices
Authors: Götze Friedrich , Kirsch Werner , Klopp Frédéric , Kriecherbauer Thomas 
Published: December 2009

It is natural to model the spectral behaviour of disordered quantum systems by the typical spectral properties of random operators. Depending on the underlying physics different kinds of ensembles have been introduced. Two types of ensembles, random Schrödinger operators and random matrices, have proved to be of particular interest because of their wide ranges of applicability and because of their rich mathematical structures. On first sight these two types of random operators may appear to be close relatives. However, as it turns out, their typical spectral properties differ significantly. Moreover, the methods that have been developed for their respective analysis have little in common. One may say that over the years two different cultures have evolved leading to two almost disjoint mathematical communities. It was the goal of this workshop to stimulate exchange between these two communities by highlighting important recent developments in both areas.
The workshop brought together 44 researchers from 9 different countries. This report contains the extended abstracts of the 30 lectures that were delivered during the meeting.
The transition from ordered to disordered system was the main topic of four lectures.
There were 14 talks about random Schrödinger operators. One of the major topics was the theory of Anderson localization/delocalization. The density of states, especially the investigation of Lifshitz tails was the subject of several contributions. The third topic in this field concerns the theory of level statistics which is a very active field at the moment. This area is much inspired by the theory of random matrices.
Twelve of the lectures were related to the theory of random matrices. In these talks a variety of ensembles, results, open problems, and methods of proof were discussed that yield a somewhat representative picture of the current state of the art in this field. The ensembles considered include the two classical cases of Wigner ensembles (independent entries) and of invariant ensembles (invariant under appropriate changes of basis). Some of the lectures dealt with more general classes of ensembles that are motivated by applications in physics and statistics. Most of the results that were presented are concerned with local correlations of eigenvalues, with the distribution of the largest eigenvalue and with (central) limit theorems for spectral quantities. One talk was devoted to the Asymmetric Simple Exclusion Process, generalizing a much celebrated result that provided a connection to random matrix theory.
Finally, it is our happy task to thank all the participants for the lively discussions, the staff of Oberwolfach for providing such perfect and pleasant working conditions and Bernd Metzger for collecting and editing the extended abstracts.
History of Mathematics of the Early 20th Century: The Role of Transition
Authors: Corry Leo , Fenster Della , Schwermer Joachim 
Published: December 2009

This conference provided a focused venue to investigate the history of mathematics during a particularly active time in the discipline, that is, roughly between the turn of the 20th century and 1950. Using the lens of transition to explore this vibrant period, the organizers brought together mathematicians, historians of mathematics and historians of science to explore ideas and offer insights from different perspectives. With this wide range of scholars in attendance, speakers had to give careful thought to the presentation of their work. This extra effort not only yielded a sterling set of talks but also inspired scholars to rethink their own work.
The restricted time period revealed an almost unexpected richness in the history of mathematics as the conference participants observed and discussed points of connection between the people, places and ideas from fields as seemingly diverse as class field theory, mathematical physics and algebraic geometry, among others. The extended abstracts below reflect the critical roles of community, politics, and institutions in the history of mathematics at this time. They also call attention to interesting questions related to the collective actions involved in transitions and the “stable” places in between.
The organizers placed an especial emphasis on the presence of and contributions by young scholars. In particular, the conference schedule included almost a full day of presentations by graduate students and recent recipients of the Ph.D. Their fresh perspective fostered a vibrant spirit during the meeting.
One of the first-time participants to Oberwolfach remarked that “this Institute has everything you need.” This “everything you need” includes the intangible components of Oberwolfach that give the most meaning to the experience. The conference participants especially appreciated the interesting mix of people and talks we enjoyed during our week at the MFO. While the idea of transition may have brought us together initially, it is the continued “mathematical talking” that will create further conversations and investigations.
Classical Algebraic Geometry
Authors: Eisenbud David , Harris Joseph , Schreyer Frank-Olaf , Vakil Ravi 
Published: December 2009

The Workshop on Classical Algebraic Geometry, organized by David Eisenbud (Berkeley), Joe Harris (Harvard), Frank-Olaf Schreyer (Saarbrücken) and Ravi Vakil (Stanford), was held June 8th to June 14th. It was attended by about 45 participants from USA, Canada, Japan, Norway, Sweden, UK, Italy, France and Germany, among of them a large number of strong young mathematicians. There were 18 talks with a maximum of four talks per day, which left plenty of time for lots of informal discussions among smaller groups.
A widespread variety of themes in classical algebraic geometry were discussed, many of them with a very modern point of view. Although it is tempting to summarize each of the talks, we limit ourselves to four highlights: