bluuebunny/crossref_metadata_2025_split huggingface dataset:
Heat Kernels, Stochastic Processes and Functional Inequalities
Authors: Coulhon Thierry , Franchi Bruno , Kumagai Takashi , Sturm Karl-Theodor 
Published: December 2009

The workshop \emph{Heat kernels, stochastic processes and functional inequalities} was organized by Thierry Coulhon (Cergy), Bruno Franchi (Bologna), Takashi Kumagai (Kyoto) and Karl-Theodor Sturm (Bonn). It was held from November 27th to December 3nd. The meeting was attended by 56 participants from Australia, Austria, Canada, Finland, France, Germany, Italy, Japan, Poland, Switzerland, United Kingdom, and USA. This workshop was sponsored by the European Union, which allowed the invitation of 18 young people, who contributed positively to the atmosphere of the meeting.

The conference brought together mathematicians belonging to several fields, essentially analysis, probability and geometry. One of the main unifying topics was certainly the study of heat kernels in various contexts: fractals, manifolds, domains of the Euclidean space, percolation clusters, infinite dimensional spaces, metric measure spaces. Some related aspects of geometric analysis were also considered such as

L^p

-cohomology and mass transportation. There was a stimulating exchange between probabilistic and analytic points of view, together with a geometric emphasis in most of the problems. We had 5 one hour survey lectures and 21 thirty-five minutes talks. A lot of time was devoted to discussions and exchange of ideas.

Among the highlights were relations between mass transportation, generalized Ricci bounds and contraction properties, connections between heat kernel estimates and percolation clusters, non-linear aspects of diffusions, functional analytic approach to parabolic regularity, geometric and functional analytic aspects of infinite dimensional analysis.
This diversity of topics and mix of participants stimulated many extensive and fruitful discussions. It also helped initiate new collaborations, in particular for the younger researchers.
Differential-Algebraic Equations
Authors: Campbell Stephen L. , März Roswitha , Petzold Linda , Rentrop Peter 
Published: December 2009

The topic of Differential Algebraic Equations (DAEs) began to attract significant research interest in applied and numerical mathematics in the early 1980's. Today, a quarter of a century later, DAEs are an independent field of research, which is gaining in importance and becoming of increasing interest for both applications and mathematical theory.
This Oberwolfach workshop brought together 48 experts in applied mathematics, among them, on the one hand, some who have already influenced and formed the developments of the field, and on the other hand, some very young researchers who have shown outstanding creativity and competence in connection with their PhD theses and thus raise great hopes for further advances.
The 16 female and 32 male scientists came from 13 countries to meet and work together in the wonderful, unique Oberwolfach atmosphere, which stimulated a fruitful and pleasant collaboration.
The schedule comprised a total of 34 presentations, 18 of which were arranged into 14 survey lectures (some of them with more than one speaker) offering a broader treatment of a particular subject. 16 shorter contributions supplemented the scientific programmme. The areas can be classified (of course with large overlap) into 4 groups:
The broad range of these areas and the diversity of the participants stimulated fruitful discussions between the different branches and gave rise to new contacts and collaborations. A considerable gain in knowledgde and progress became obvious, which includes the formulation of open questions and challenges for the future.
We are grateful to the Mathematisches Forschungsinstitut Oberwolfach for providing an inspiring setting for this workshop.
Feinstrukturtheorie und Innere Modelle
Authors: Jensen Ronald B. , Magidor Menachem , Schindler Ralf-Dieter 
Published: December 2009

The workshop
Fine Structure Theory and Inner Models
, organised by Ronald Jensen (Berlin), Menachem Magidor (Jerusalem) and Ralf Schindler (Münster) was held April 30th - May 6th, 2006. It was attended by most of the leading researchers in the area.

Fine structure theory was initiated by the first organizer, R. Jensen, in the 70ies. It has been exploited ever since for producing a series of spectacular results in set theory. One such is Jensen's Covering Lemma for Gödel's constructible hierarchy,

L

, which says, put informally, that the universe

V

of all sets either resembles

L

to a large extent or else is very different from

L

. Later on, various people (most of which were participants of this workshop) proved versions of the Covering Lemma for larger inner models.

The main goal of “Fine structure theory and inner model theory” is to construct fine structural inner models of set theory, i.e., definable transitive proper class-sized models of the standard axiom system

{\sf ZFC}

of set theory, which reflect the large cardinal structure of the universe, but at the same time admit a fine structure that makes it possible to analyze them in great detail and prove various combinatorial properties in them. Other applications of such inner models are consistency strength investigations, and they can be used as a tool for proving implications which don't mention inner models at all, but for which no “direct” proof is in sight.

A large cardinal concept is one such that

\mathsf{ZFC}

cannot prove that there is an incarnation of it. Our area is the key tool for uncovering the large cardinal structure which is implicit in many (not only set theoretic) hypotheses. In fact, often a given statement which doesn't mention large cardinals at all and a statement about the existence of models with large cardinals turn out to be two sides of the same coin. Breathtaking results by Martin, Steel, Woodin, and others in the 80ies and 90ies have shown that the large cardinal concept of a
Woodin cardinal
is a crucial one here.

The main issues of this area are the following.
The conference had 16 participants. 13 talks were given, and they covered both pure and applied parts of inner model theory. Because this was a gathering of true specialists, there was no need for overview-style talks and we could concentrate on issues which are at the focus of current research. The talks came with intriguing results, but also with promising new perspectives for upcoming research. We had very lively discussions.
It was a fruitful workshop, and many of the ideas which were exchanged are sure to be further elaborated in the near future.
Geometric and Topological Combinatorics
Authors: Björner Anders , Kalai Gil , Ziegler Günter M. 
Published: December 2009

The 2007 Oberwolfach meeting “Geometric and Topological Combinatorics” was organized by Anders Björner (KTH and Mittag-Leffler Institute, Stockholm), Gil Kalai (Hebrew University, Jerusalem), and Günter M. Ziegler (TU Berlin). It consisted of six one-hour lectures by Isabella Novik, Herbert Edelsbrunner, Carsten Schultz, Igor Pak, Alexander Barvinok and Roy Meshulam, as well as twenty-seven half-hour talks, a problem session (led by Gil Kalai, also documented below), two software demonstrations (on by Michael Joswig, and on by Jesus De Loera), and many more informal sessions, group discussions, and a great variety of small group and pairwise discussions. It was a lively week!
As will become obvious from the sequence of extended abstracts presented below, the conference treated a broad spectrum of topics from Topological Combinatorics (such as poset topology, graph coloring, etc.), Discrete Geometry (polytopes, triangulations, arrangements, Coxeter groups, and polyhedral surfaces), as well as Geometric Topology (triangulated manifolds, persistent homology of geometric data, etc.).

The manifold connections between these themes, with refinements of well-established bridges as well as completely new links between seemingly distant themes, problems, methods, and theories show that the area is very much alive. Even more so this is demonstrated by substantial progress on older problems, which on this conference included Isabella Novik's opening lecture about centrally symmetric polytopes (joint works with Nati Linial and with Alexander Barvinok), or still on the first day Ed Swartz' report about the

f

-vectors of triangulated manifolds.

Of course there is no way to present the richness and depth of the work and presentations of the conference's program on a one page report, or a short collection of abstracts. All the following can offer is an overview of the official program of the conference. It does not cover all the additional smaller presentations, group discussions and blackboard meetings (for example, Tom Braden was coerced into an additional evening presentation of the topology of hypertoric varieties “by popular demand”), nor the lively interactions that occured during the week – for example, a surprising connection was made at the problem session between permutation patterns that appeared in Jonas Sjöstrand's lecture, and a conjecture posed by Alex Postnikov; in subsequent work, the problem was solved by Axel Hultman, Svante Linusson, John Shareshian, and Jonas Sjöstrand (paper in preparation). We are extremely grateful to the Oberwolfach institute, to its director and to all of its staff for providing a perfect setting for an inspiring, intensive week of “Geometric and Topological Combinatorics.”
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 equation 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 modeling applications. The latter judgment 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, in fact quite distinct from the snap-shot taken exactly three years ago. A partial list of topics reads
We had 44 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.
Modulformen
Authors: Böcherer Siegfried , Ibukiyama Tomoyoshi , Kohnen Winfried 
Published: December 2009

The workshop
Modulformen
, organised by Siegfried Böcherer (Mannheim), Tomoyoshi Ibukiyama (Osaka) and Winfried Kohnen (Heidelberg) was held October 28–November 3, 2007. This meeting was attended by 24 participants with different backgrounds reflecting some of the many aspects of the theory of modular forms. One of the callenging features of this theory is that techniques using Whittaker models do not apply here. On the other hand, the theory is very rich in explicit structures and has immediate connections to arithmetic and geometry.

Some of the main topics (presented in one-hour talks) are

The third and forth topic are not only interesting in their own right but they are also a testing ground for general conjectures. We explictly mention the theory of newforms by Roberts and Schmidt for

GSp(4)

.

Explicit liftings can be viewed as examples for Langlands functoriality. The emphasis is on the explicit description of these liftings in terms of modular forms (not only representations). A prototype is the Duke–Imamoglu–Ikeda-lifting, which appeared in several talks.
Other talks dealt with theta series, Poincare series, generation of spaces of modular forms, converse theorems and spherical functions on p-adic spaces. Beyond the talks, there was much opportunity for scientific interaction among the participants.
Arbeitsgemeinschaft: Julia Sets of Positive Measure
Authors: Buff Xavier , Cheritat Arnaud 
Published: December 2009

A polynomial

P:\mathbb C\to :\mathbb C

can be considered as a dynamical system. We are interested in the sequences

(z_n)

defined by induction:

z_0\in :\mathbb C\quad\text{and}\quad z_{n+1}=P(z_n).

The filled-in Julia set

K_P

is the set of points

z_0\in :\mathbb C

for which the sequence

(z_n)

is bounded. This set is compact. The Julia set

J_P

is the boundary of

K_P

. In particular, it has empty interior. There is a small collection of polynomials, for instance

P(z) = z^d\quad ,\quad P(z) = z^2-2,

for which the Julia set can be fairly easily understood, but most exhibit “fractal” geometry and “chaotic” behavior, the analysis of which requires serious tools from complex analysis, dynamical systems, topology, combinatorics,

\ldots

This subject has a fairly long history, with contributions by Koenigs, Schröder, Böttcher in the late 19th century, and the great memoirs of Fatou and Julia around 1920.
There followed a dormant period, with notable contributions by Cremer (1936) and Siegel (1942), and a rebirth in the 1960's (Brolin, Guckenheimer, Jakobson). Since the early 1980's, partly under the impetus of computer graphics, the subject has grown vigorously, with major contributions by Douady, Hubbard, Sullivan, Thurston, and more recently Lyubich, McMullen, Milnor, Shishikura, Yoccoz \ldots

Fatou found sufficient conditions for the boundary of the basin of an attracting fixed point to be a Cantor set with Lebesgue measure equal to

0

. He could not tell whether or not the measure could be positive.

For some time and until the 1990's, the conjecture, reinforced by the analogy with Ahlfors's conjecture on the area of limit sets of Kleinian groups, was that no Julia set of a polynomial could have positive area.
Results in this direction were obtained by Douady and Hubbard in the case of hyperbolic or subhyperbolic maps, by Branner, Hubbard and McMullen in the case of non-renormalizable cubic polynomials with an escaping critical point, by Lyubich and Shishikura in the case of finitely renormalizable quadratic polynomials without indifferent cycles, by Petersen in the case of quadratic polynomials having a Siegel disk with bounded type rotation number.
In the 1990's, Douady began to catch a glimpse of a method for Julia sets of positive area: in the family of degree 2 polynomials with an indifferent Cremer fixed point. Recently, we brought Douady's method to completion.

The Arbeitsgemeinschaft
Julia sets of positive measure
focused on the proof of existence of quadratic polynomials having a Julia set of positive area. It was held March 30th–April 5th, 2008. It was attended by 36 participants.
Atomistic Models of Materials: Mathematical Challenges
Authors: E Weinan , Friesecke Gero , Pettifor David 
Published: December 2009

The past decades have witnessed an explosion of interest in the application of mathematical models to science and engineering down at the atomic scale. Atomistic models are large, complex, multiscale, and in particular discrete, and provide a rich source of fascinating challenges for mathematics. In particular, a basic goal is to understand (1) how and at which length- and timescales the behaviour of large atomistic systems becomes well approximated by traditional continuum descriptions (of dislocations, grains, fracture, elasticity or plasticity), and under which circumstances atomistic and continuum “modes” are nontrivially coupled (2) how atomistic models can be accurately and efficiently extracted from quantum mechanical models.
While mathematical research in this area is still in its early stages, interest by mathematicians in atomistic models is fast growing, and the goal of this workshop was to bring together leading mathematicians and materials scientists, in the unique Oberwolfach setting, in order to document recent results, discuss main open challenges, and stimulate an exchange between the two communities.
The workshop focused on the following topics, the basic goals described above being recurrent themes.
The organizers are particularly indebted to the participants from both mathematics and materials science for making such a committed effort to communicate their work to researchers from the other community, both in the actual talks and in this Oberwolfach report. Judging by the success of this effort, we are confident that this report can serve as a starting point and a stimulation for a great deal of future interaction between our communities.
Real Analysis, Harmonic Analysis and Applications
Authors: Müller Detlef , Stein Elias M. 
Published: December 2009

This workshop, which continued the triennial series at Oberwolfach on Real and Harmonic Analysis that started in 1986, has brought together experts and young scientists working in harmonic analysis and its applications (such as to dispersive PDE's and ergodic theory) with the objective of furthering the important interactions between these fields.
Three prominent experts, Elon Lindenstrauss (Princeton), Amos Nevo (Technion, Haifa), and Terence Tao (UCLA), gave survey respectively introductory lectures. Their topics included “Effective equidistribution on the torus”, “Non-Euclidean lattice point counting problems, and the ergodic theory of lattice subgroups,” and “The van der Corput lemma, equidistribution in nilmanifolds, and the primes.”
Major further areas and results represented at the workshop are:
The meeting took place in a lively and active atmosphere, and greatly benefited from the ideal environment at Oberwolfach. It was attended by 43 participants. The program consisted of 3 survey lecture series and 25 lectures. The organisers made an effort to include young mathematicians, and greatly appreciate the support through the joint Oberwolfach/NSF program “US Junior Oberwolfach Fellows,” which allowed to invite several outstanding young scientists from the United States.
Geometrie
Authors: Taimanov Iskander A. , Wilking Burkhard , Lott John 
Published: December 2009

The official program consisted of 20 lectures and therefore left plenty of space for fruitful informal collaboration for the 44 participants. One emphasis with 9 talks at this meeting was on geometric flows. Exciting progress could be reported on
Another important theme was metric and Finsler geometry with five talks covering the following topics
The other six talks covered other aspects of geometry including
Several connections between the different areas became apparent during the workshop. For example, the initial value problem for the Ricci flow with singular initial data is closely linked to smoothing problems occuring in Alexandrov geometry.
Discrete Geometry
Authors: Henk Martin , Matoušek Jiří , Welzl Emo 
Published: December 2009

Discrete Geometry
deals with the structure and complexity of discrete geometric objects ranging from finite point sets in the plane to more complex structures like arrangements of

n

-dimensional convex bodies. Classical problems such as Kepler's conjecture and Hilbert's third problem on decomposing polyhedra, as well as classical works by mathematicians such as Minkowski, Steinitz, Hadwiger and Erdös are part of the heritage of this area. By its nature, this area is interdisciplinary and has relations to many other vital mathematical fields, such as algebraic geometry, topology, combinatorics, computational geometry, convexity, and probability theory. At the same time it is on the cutting edge of applications such as geographic information systems, mathematical programming, coding theory, solid modelling, computational structural biology and crystallography.

The workshop was attended by 40 participants. There was a series of 12 survey talks giving an overview of developments in Discrete Geometry and related fields:
In addition, there were 18 shorter talks and an open problem session chaired by János Pach on Wednesday evening — a collection of open problems resulting from this session can be found in this report. The program left ample time for research and discussions in the stimulating atmosphere of the Oberwolfach Institute.
Polymorphisms in KCNE1 or KCNE3 are not associated with Ménière disease in the Caucasian population
Authors: Campbell Colleen A. , Della Santina Charley C. , Meyer Nicole C. , Smith Nancy B. , Myrie Oluwaseun A. , Stone Edwin M. , Fukushima Kuni , Califano Joseph , Carey John P. , Hansen Marlan R. , Gantz Bruce J. , Minor Lloyd B. , Smith Richard J.H. 
Published: December 2009

AbstractMénière disease (MD) is a complex disorder of unknown etiology characterized by the symptom triad of vertigo, sensorineural hearing loss, and tinnitus. Its reported incidence is 1–2 per 1,000 in Caucasians and 0.03–0.37 per 1,000 in Japanese. Doi et al. [Doi et al. (2005); ORL J Otorhinolaryngol Relat Spec 67:289–293] recently reported that two single nucleotide polymorphisms (SNPs) in KCNE1 and KCNE3 are associated with MD in Japanese subjects. Consistent with this possibility, these two genes encode potassium channels that are expressed in the stria vascularis and endolymphatic sac, respectively, and their role in ion transport suggests that they may be important in inner ear homeostasis. To establish whether a similar association exists in the Caucasian MD population, we sequenced the coding regions and exon–intron boundaries of both genes in 180 Caucasian persons with MD and 180 matched Caucasian controls. Neither of the two reported SNPs was significantly associated with MD when compared to the Caucasian controls (KCNE1, P = 0.55; KCNE3, P = 0.870). Comparison of allele frequencies between the Japanese MD population and our study population revealed no significant difference between groups (KCNE1, P = 0.90; KCNE3, P = 0.862), suggesting that the significant differences reported in the Japanese study arose from their control population. Six additional SNPs in both KCNE1 and KCNE3 were genotyped and none was associated with MD. Population stratification within our MD and Caucasian control population was excluded. Our data show that SNPs in KCNE1 and KCNE3 are not associated with MD in Caucasians. © 2009 Wiley‐Liss, Inc.