bluuebunny/crossref_metadata_2025_split huggingface dataset:
Large Scale Stochastic Dynamics
Authors: Landim Claudio , Olla Stefano , Spohn Herbert 
Published: December 2009

“Large Scale Stochastic Dynamics” is at the crossroad of probability theory and statistical physics. One central theme of statistical physics is the emergent behavior resulting from the interaction of many identical components, the paradigm being a fluid or a gas. On the atomistic scale they consist of a huge number of identical molecules. Their motion is governed by Newton's equations of classical mechanics (ignoring quantum effects). The emergent description, valid only for particular initial states and on a sufficiently coarse space-time scale, are the compressible Navier-Stokes equations of fluid dynamics. Roland Dobrushin (1929–1995) and Frank Spitzer (1926–1992) had the vision that in the context of stochastic dynamics with many identical components the issue of emergent behavior is both mathematically challenging and important in modelling applications. The latter judgement turned out to be more than true. Stochastic algorithms, such as kinetic Monte Carlo, importance sampling, Monte Carlo Markov chains, Glauber dynamics, and others, are daily practice. Their mathematical vision has evolved over the past twenty years into a rich, multifaceted research program. Our workshop is like a snap-shot of the current activities. A partial list of topics reads
We had 49 participants from 11 countries, mostly probabilists, but also experts from partial differential equations and statistical physics. They all enjoyed tremendously the unique and stimulating atmosphere at the Mathematische Forschungsinstitut Oberwolfach and hope to return some day.
Polylogarithms
Authors: Bloch Spencer , Kings Guido , Wildeshaus Jörg 
Published: December 2009

The

k

-th polylogarithm function is defined on

|z|<1

by

Li_k(z) = \sum_{n\geq 1} \frac{z^n}{n^k}.

In the past 25 years or so, polylogarithms have appeared in many different areas of Mathematics. The following list is taken, for the most part, from [Oe]: volumes of polytopes in spherical and hyperbolic geometry, volumes of hyperbolic manifolds of dimension 3, combinatorial description of characteristic classes, special values of zeta functions, geometry of configurations of points in

\mathbb P^1

, cohomology of

GL_n(\mathbb C)

, calculation of Green's functions associated to perturbation expansions in quantum field theory, Chen iterated integrals, regulators in algebraic

K

-theory, differential equations with nilpotent monodromy, Hilbert's problem on cutting and pasting, nilpotent completion of

\pi_1(\mathbb P^1-\{0,1,\infty\})

, Bethe's Ansatz in thermodynamics, and combinatorial problems in quantum field theory.

Of course, these problems are not all unrelated. One common thread is that values of polylogarithms appear naturally as periods of certain mixed Hodge structures associated to mixed Tate motives over cyclotomic fields. How these periods are related to special values of

L

-functions is a part of the Beilinson conjectures, which were discussed in a previous Arbeitsgemeinschaft. Since that time, the general picture has clarified. A number of talks are devoted to aspects of this more general philosophy (talk 2-5, 9, 10 13-17). The

p

-adic aspects of the theory have been studied and will be explained in the eleventh talk. In addition, a vast generalization, multiple polylogarithms of the form

Li_{s_1,\dotsc,s_k} := \sum_{n_1>\ldots > n_k \geq 1} \frac{z_1^{n_1}\cdots z_k^{n_k}}{n_1^{s_1}\cdots n_k^{s_k}},

have come to play a role as presented in the fourth and twelfth talk.
The connection between volumes of hyperbolic manifolds and polylogarithms is described in the sixth talk. The seventh talk introduces higher torsion and explains why polylogarithms occur in that setting.
Polylogarithms play a role in physics. The eighth talk explains how zeta values, polylogarithms, and multiple polylogarithms appear in calculations of perturbative expansions in quantum field theory.

The final talks 13-17 return to the relationship with special values of

L

-functions. The thirteenth and fourteenth talk are devoted to the Zagier conjectures for number fields. The fifteenth talk concerns the elliptic polylogarithm sheaves and Zagier's conjecture for elliptic motives. Finally, talk 16 and 17 describe how polylogarithms relate to Euler systems and to the Bloch-Kato conjectures on special values of

L

-functions.

The
Arbeitsgemeinschaft
was organized by Spencer Bloch (University of Chicago), Guido Kings (Universität Regensburg) and Jörg Wildeshaus (Université Paris 13). It was held October 3rd – October 9th, 2004 with 46 participants.
Nonlinear Waves and Dispersive Equations
Authors: Kenig Carlos E. , Koch Herbert , Tataru Daniel 
Published: December 2009

Nonlinear dispersive equations are models for nonlinear waves in a wide range of situations. Mathematically they display an interplay between linear dispersion and nonlinear focusing or defocusing effects. They are linked to diverse areas of mathematics and physics, ranging from nonlinear optics over oscillatory integrals and integrable systems to algebraic geometry. The conference did focus on the analytic (PDE) aspects with a view towards applications.
Major results and areas are:
Motivated by recent developments there has been a series of lectures by T. Kappeler and P. Topalov on their application of the inverse scattering transform to rough initial data for the Korteweg-de-Vries equation.
This meeting was attended by 45 participants. The organizers made an effort to include young mathematicians and to give them the opportunity of a shorter talk.
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 49 participants. In an age range between the early 20's and the late 50's, there were young PhD students, together with established leaders of the fields which are related to the not too specialized thematic title of the workshop. There were 23 talks, each one lasting 50 minutes but followed by a lively 10-15 minutes discussion, which as usual continued outside the lecture room and 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 last, cf. the survey of Jun Li on Gromow Witten invariants). The more detailed contents of the several expositions can be suitably grouped under the following general headings :
The style of the talks varied considerably, ranging from general overviews like the one by Corti, to “experimental” conjectures, like the ones given by Schreyer, but the variety of striking results and very interesting and challenging proposals is so great that certainly each organizer and each participant had its favourite ones. We believe however that the quality of the expositions in the abstracts collected here is such that we do not deem it necessary to further procrastinate the anticipated pleasure of the reader.
Regelungstheorie
Authors: Allgöwer Frank , Helmke Uwe , Kwakernaak Huibert 
Published: December 2009

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering. It therefore covers a wide variety of topics, ranging from fundamental mathematical aspects to real world engineering applications of industrial relevance. In particular, it has deep connections to different branches of pure and applied mathematics, including e.g. operator theory, real and complex analysis, probability theory, commutative algebra, as well as algebraic and differential geometry.
The Oberwolfach workshop “Regelungstheorie” has the traditional goal of bringing active researchers with both a mathematical and an engineering background together in order to stimulate a fruitful interaction between these communities. This diversity of our field was once again nicely reflected in the expertise of the 42 participants of the 2005 workshop from all over the world. A particular effort has been devoted to inviting newcomers from the somewhat younger generation which had the refreshing side-effect of an increase in the number of female participants.
The particular mission of the workshop was as well reflected in the various themes that have been addressed in the 29 stimulating presentations. The program has been clustered into rather coherent sessions of three lectures each revolving around
In addition to regular session talks of thirty minutes, each day was initialized with a somewhat longer presentation that was followed by a five-minute discussant statement. This novel feature provided an extra stimulus for lively general discussions during the subsequent coffee breaks and beyond.
As a particular highlight, Vincent Blondel and Jan Willems organized and chaired a session on open problems in systems and control on Tuesday evening. Eight contributors had the opportunity to present concrete research questions in seven minutes, followed by a brief two minutes discussion with the audience. Six of the corresponding abstracts related to the open problems have been collected at the end of this report and should, in view of the raised challenges, stimulate lots of new research initiatives.
In addition to the excellent scientific program most participants could as well enjoy the traditional Wednesday afternoon walk to St. Roman, with beautiful weather and in a wonderful winter landscape. The day was concluded by an impressive musical evening with excerpts from Schubert's “Winterreise” presented by P. Hippe (bariton) and P. Lohmann (piano).
Partielle Differentialgleichungen
Authors: Ilmanen Thomas , Schätzle Reiner , Trudinger Neil S. 
Published: December 2009

The workshop
Partial differential equations
, organised by Tom Ilmanen (ETH Zürich), Reiner Schätzle (Universität Tübingen) and Neil Trudinger (Australian National University Canberra) was held July 24-30, 2005. This meeting was well attended by 46 participants, including 6 females, with broad geographic reprensentation. The program consisted of 15 talks and 9 shorter contributions and left sufficient time for discussions.

New results combining partial differential equations and geometric problems were presented in the area of minimal surfaces, free boundaries and singular limits, for example the construction of branched minimal surfaces, the regularity of free boundaries in the wake of the monotonicity formula of Weiss and a proof of a conjecture of De Giorgi.
A major part of the leading experts of partial differential equations with conformal invariance attended the workshop. Here new results were presented in conformal geometry, for the Yamabe problem, the Paneitz operator and the Willmore functional.
Dynamical System Methods in Fluid Dynamics
Authors: Marsden Jerrold E. , Scheurle Jürgen 
Published: December 2009

The workshop was organized around the following classical as well new and emerging techniques. Traditional methods in fluid mechanics continue to be invigorated with the infusion of ideas from dynamical systems, geometric methods, multiscale analysis, new developments in scientific computation, and control theory. The specific themes of the workshop were as follows:

Structure of the Meeting.
The meeting had a balance of senior researchers, postdoctoral fellows and graduate students. Consistent with the general approach advocated by Oberwolfach, we selected about 20–25 people to give a lecture at the meeting. They suggested students, postdoctoral fellows and junior faculty all of whom participated through two poster sessions.

Posters.
The poster session was one of the most interesting aspects of the meeting. The organizers decided to award prizes for the best poster and an ad hoc committee (consisting of Friedlander, Haller, Reich, Marsden and Scheurle) was formed to choose the four best posters. This number matched the number of gifts that were available. The winners were (in alphabetical order):

Impressions, Connections, Insights.
The mixture of participants, from those who were very applied and those who came from a more of a dynamical systems background, but all with a strong mathematical dedication, was very fruitful.

Dynamical systems methods have now started to be utilized successfully for the study of complex real fluid systems, from controlled man-made experiments to multi-scale and multivariate natural dynamics, from oceanic motions to flows around jellyfish. Dynamical system approaches are then applied to complex data, models or combinations thereoff. There is a wide range of research opportunities, including the possibilty for new theoretical and methodological progress.
Amongst the specific new connections and insights that were gained, the power of dynamical systems ideas, such as invariant manifolds or Lyapunov exponents, seemed to be quite impressive as well as useful in the context of metereology as well as oceanography. The use of dynamical systems ideas in control of fluids (separation and cavity oscillations, for example) was also quite interesting for a number of the participants.
Mini-Workshop: Analysis and Computation of Microstructures in Finite Plasticity
Authors: Hackl Klaus , Conti Sergio , Ortiz Michael 
Published: December 2009

The miniworkshop was attended by fourteen participants of whom twelve gave presentations. Additionally Kolumban Hutter from the University of Darmstadt, then at the research institute as a research-in-pairs fellow, agreed to give a talk on “Granular flows and avalanches”. There was one discussion session chaired by Stefan Müller, during which the most important problems of the field which have to be addressed in the near future were identified. The individual talks lasted for one and a half hours in the average and were interlaced with lively discussions.
The main theme in the workshop was the variational formulation of crystal plasticity, in a rate-independent setting. For small time-intervals, this leads to a single variational problem, which is often referred to as the “first time step”. One substantial difficulty arises from the fact that the resulting functional is not lower semicontinuous, leading to non-existence of minimizers. The corresponding theory of relaxation has some analogies to the one developed in nonlinear elasticity. A second issue is the formulation of a theory that goes beyond small time intervals. In a framework where time is discretized, the functional at each time step depends on the minimizer at the previous one (assuming it exists). This leads to a sequence of coupled variational problems, and even the precise definition of the time-continuous limit is not yet completely understood.
The subjects treated ranged from the mathematical formulation of the variational problems and existence results for those, to analytical and numerical methods to determine their relaxation, and applications to various problems in mechanics and physics. Research in progress and sometimes of speculative nature was presented rather then established results. Specifically, the main questions treated were the following:
During the miniworkshop progress could be made concerning some of these questions and interesting ideas where developed for the rest of them.
The Arithmetic of Fields
Authors: Geyer Wulf-Dieter , Jarden Moshe , Pop Florian 
Published: December 2009

The fifth conference with the title
The Arithmetic of Fields
, organized by Wulf-Dieter Geyer (Erlangen), Moshe Jarden (Tel Aviv), and Florian Pop (Philadelphia), was held February 5–11th, 2006. In contrast to the fourth conference held in February 3–9th, 2002, this conference was a “full” one, namely as many participants were invited as the Institute could host. Due to support from the European Union, more young people were invited in the last few weeks prior to the conference, so that the total number of participants reached 54. The participants came from 13 countries: Germany (20), USA (10), Israel (7), France (7), Denmark (2), Austria (1), Brazil (1), Canada (1), Hungary (1), Japan (1), Romania (1), Russia (1), and South Africa (1). Among the participants there were 9 graduate students and 8 young researchers. Six women attended the conference.

The organisers asked four people before the conference to give surveys of one hour on recent progress made by other colleagues in Field Arithmetic.

Tamás Szamuely (Budapest) reported on the solution by János Kollár of a Problem due to Ax from 1968: Every PAC field of characteristic

0

is

C_1

. The case where the characteristic is positive remains open.

Alexandra Shlapentokh (Greenville) described the progress Bjorn Poonen made on Hilbert's Tenth Problem: There exists a recursive set

T_1

of prime numbers of natural density

0

and a set

T_2

of prime numbers of natural density

1

such that

T_1\subseteq T_2

and for each set

S

with

T_1\subseteq S\subseteq T_2

Hilbert's Tenth Problem for

O_{\mathbb Q,S}

has a negative solution. Here

O_{\mathbb Q,S}

is the ring of all rational numbers whose denominators are divided only by primes in

S

. Whether Hilbert's Tenth Problem for

\mathbb Q

has a negative solution is still open.

Alexander Prestel (Konstanz) presented a theorem of Jochen Koenigsmann: If a

p

-Sylow extension

P

of a field

K

is Henselian and

P

is neither separably closed nor real closed, then

K

itself is Henselian.

Pierre Débes (Lille) surveyed Fried's problem on Modular Towers. He mentioned that the main conjecture is close to completion in the case of

4

branch points (Bayley–Fried). He also reported on a result of Anna Cadoret: The dihedral group has a regular realization over

\mathbb Q_{\rm ab}

with only inertia groups of order

2

.

In addition to these survey talks seventeen participants were invited to report on their own achievements in 45 minutes talks. Altogether, the talks presented the impressive progress made in Field Arithmetic in recent years. The reader may find here extended abstracts of all talks. We hope they will be to the benefit of all of the participants as well as the fans of Field Arithmetic.
The organisers: Wulf-Dieter Geyer, Moshe Jarden, Florian Pop
Numerical Techniques for Optimization Problems with PDE Constraints
Authors: Heinkenschloss Matthias , Hoppe Ronald H.W. , Schulz Volker 
Published: December 2009

The numerical solution of optimization problems with partial differential equation (PDE) constraints is vital to a growing number of science and engineering applications. The development of robust and efficient algorithms for the solution of these optimization problems presents many challenges that arise out of, e.g., the intricate mathematical structure of these problems, the complicated interactions between numerical methods for PDE and optimization, the large-scale of the optimization problems, and the increasing complexity of applications. To identify and overcome these challenges an integrated approach is needed that builds on a variety of mathematical sub-disciplines, such as theory of PDEs, distributed parameter systems, numerical solution of PDEs, numerical optimization, and numerical linear algebra. This international workshop has brought together some of the leading experts in the fast developing field of optimization problems with PDE constraints to present recent developments in this area as well as to identify open problems and further research needs.
Among the themes of this workshop were the design and analysis of approaches for the solution of PDE constrained optimization problems with additional point-wise constraints on controls and states (the solution of the governing PDE). State constrained problems are particularly challenging because of the low regularity properties of the Lagrange multipliers associated with point-wise constraints on the states. A second theme was the development of adaptive methods for the solution of PDE constrained optimization problems and, more generally, the development of optimization level model reduction techniques for these problems. The goal here is to develop models (through, e.g., mesh adaptation or proper orthogonal model reduction) of the PDE constrained optimization problems that capture the relevant features of the optimization problems with a specified accuracy, but involve as few degrees of freedom as possible and, hence, are computationally less expensive to work with. A third theme was The efficient solution of linear systems arising in optimization algorithms for discretized PDE constrained optimization problems represented another theme. Finally, a number of talks presented advances and challenges in the solution of PDE constrained optimization problems arising in important science and industrial applications.
Analysis and Topology in Interaction
Authors: Bunke Ulrich , Goette Sebastian , Igusa Kiyoshi , Schick Thomas 
Published: December 2009

The MFO workshop “Analysis and Topology in Interaction”, organised by Ulrich Bunke (Göttingen), Sebastian Goette (Regensburg), Kyoshi Igusa (Brandeis) and Thomas Schick (Göttingen), was held from March 12th through March 18th, 2006.
The aim of this meeting was to reflect on the current state of the interaction between mathematical fields of analysis and topology. It brought together representatives of various mathematical communities ranging from homotopy theory, index theory, global analysis up to mathematical physics. The program of the conference has been a mixture of research and overview talks, sometimes with introductory elements. Topics of the latter kind were the connection of Quantum field theory constructions with twisted K-theory, and motivic groups. There were two more informal introductory lectures on stacks in topological and smooth categories, and the insights given by the study of the Brownian motions into Hodge theory.
The research talks reflected recent developments in the corresponding fields and covered a broad area between topology, geometry, and analysis. The intention of the program was to communicate these developments across the borders of mathematical communities. They stimulated discussions and hopefully future collaborations.
More specifically, the subjects covered by research talks included in particular
Altogether, there were 23 “official” talks and a number of informal presentations (partly extended discussions), and ample free interaction between the participants. One of the evenings was devoted to a problem session; the open problems presented are included in this report.
The conference was attended by 52 participants coming mainly from all over Europe, Northern America and East Asia. Among them, a couple of very young pre-doctoral mathematicians, supported by the EU, had the unique opportunity to participate in such a stimulating event at a very early stage of their career. It is a pleasure to thank the institute for providing a pleasant and stimulating atmosphere.