Oberwolfach Reports (OWR)

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4-dimensional Manifolds
(Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 2001) Kronheimer, Peter B.; Stern, Ronald J.
[no abstract available]
Actions and Invariants of Residually Finite Groups: Asymptotic Methods
(Zürich : EMS Publ. House, 2010) Gaboriau, Damien; Grunewald, Fritz
The workshop brought together experts in finite group theory, L2-cohomology, measured group theory, the theory of lattices in Lie groups, probability and topology. The common object of interest was residually finite groups, that each field investigates from a different angle.
Adaptive Algorithms
(Zürich : EMS Publ. House, 2016) Stevenson, Rob
Overwhelming empirical evidence in computational science and engineering proved that self-adaptive mesh-generation is a must-do in real-life problem computational partial differential equations. The mathematical understanding of corresponding algorithms concerns the overlap of two traditional mathematical disciplines, numerical analysis and approximation theory, with computational sciences. The half workshop was devoted to the mathematics of optimal convergence rates and instance optimality of the Dörfler marking or the maximum strategy in various versions of space discretisations and time-evolution problems with all kind of applications in the efficient numerical treatment of partial differential equations.
Adaptive Numerical Methods for PDEs
(Zürich : EMS Publ. House, 2007) Süli, Endre; Verfürth, Rüdiger
This collection contains the extended abstracts of the talks given at the Oberwolfach Conference on “Adaptive Numerical Methods for PDEs”, June 10th - June 16th, 2007. These talks covered various aspects of a posteriori error estimation and mesh as well as model adaptation in solving partial differential equations. The topics ranged from the theoretical convergence analysis of self-adaptive methods, over the derivation of a posteriori error estimates for the finite element Galerkin discretization of various types of problems to the practical implementation and application of adaptive methods.
Adaptive Statistical Inference
(Zürich : EMS Publ. House, 2014) Munk, Axel; Tsybakov, Alexandre
This workshop in mathematical statistics highlights recent advances in adaptive methods for statistical estimation, testing and confidence sets. Related open mathematical problems are discussed with potential impact on the development of computationally efficient algorithms of data processing under prior uncertainty. Parcticular emphasis is on high dimensional models, inverse problems and discrtete structures.
Advanced Computational Engineering
(Zürich : EMS Publ. House, 2012) Carstensen, Carsten; Schröder, Jörg; Wriggers, Peter
The finite element method is the established simulation tool for the numerical solution of partial differential equations in many engineering problems with many mathematical developments such as mixed finite element methods (FEMs) and other nonstandard FEMs like least-squares, nonconforming, and discontinuous Galerkin (dG) FEMs. Various aspects on this plus related topics ranging from order-reduction methods to isogeometric analysis has been discussed amongst the pariticpants form mathematics and engineering for a large range of applications.
Affine Algebraic Geometry
(Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 2000) Kraft, Hanspeter; Russell, Peter
[no abstract available]
Affine Algebraic Geometry
(Zürich : EMS Publ. House, 2007) Russell, Peter; Zaidenberg, Mikhail
Aﬃne geometry deals with algebro-geometric questions of aﬃne varieties that are treated with methods coming from various areas of mathematics like commutative and non-commutative algebra, algebraic, complex analytic and diﬀerential geometry, singularity theory and topology. The conference had several main topics. One of them was the famous Jacobian problem, its connections with the Dixmier conjecture and possible algebraic approaches and reductions. A second main theme were questions on Log algebraic varieties, in particular log algebraic surfaces. Thirdly, results on automorphisms of An played a major role, in particular the solution of the Nagata problem, actions of algebraic groups on An , Hilbert’s 14th problem and locally nilpotent derivations. More generally automorphism groups of aﬃne and non-aﬃne varieties, especially in dimension 2 and 3 were treated, and substantial progress on the cancelation problem and embedding problem was presented.
Algebraic Cobordism and Projective Homogeneous Varieties
(Zürich : EMS Publ. House, 2016) Levine, Marc; Panin, Ivan; Vishik, Alexander
The aim of this workshop was to bring together researchers in the theory of projective homogeneous varieties with researchers working on cohomology theories of algebraic varieties, so that the latter can learn about the needs in an area of successful applications of these abstract theories and the former can see the latest tools.
Algebraic Geometry
(Zürich : EMS Publ. House, 2015) Huybrechts, Daniel; Kawamata, Yujiro; Siebert, Bernd
The workshop covered a broad variety of areas in algebraic geometry and was the occasion to report on recent advances and works in progress. Special emphasis was put on the role of derived categories and various stability concepts for sheaves, varieties, complexes, etc. The mix of people working in areas like classification theory, mirror symmetry, derived categories, moduli spaces, $p$-adic geometry, characteristic $p$ methods, singularity theory led to stimulating discussions.
Algebraic Geometry: Birational Classification, Derived Categories, and Moduli Spaces
(Zürich : EMS Publ. House, 2017) Huybrechts, Daniel; Siebert, Bernd; Xu, Chenyang
The workshop covered a number of active areas of research in algebraic geometry with a focus on derived categories, moduli spaces (of varieties and sheaves) and birational geometry (often in positive characteristic) and their interactions. Special emphasis was put on hyperkähler manifolds and singularity theory.
Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects
(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2022) Hacon, Christopher; Huybrechts, Daniel; Thomas, Richard; Xu, Chenyang
The workshop covered recent developments in algebraic geometry in a broad sense with a special emphasis on various moduli spaces. Problems related to mirror symmetry phenomena were discussed in a number of talks as well as singularity theory in the context of the MMP in positive characteristic. Derived categories and algebraic cycles, as well as rationality questions figured prominently in the talks and the discussions.
Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (hybrid meeting)
(Zürich : EMS Publ. House, 2020) Huybrechts, Daniel; Thomas, Richard; Xu, Chenyang
The talks at the workshop and the research done during the week focused on aspects of algebraic geometry in the broad sense. Special emphasis was put on hyperkähler manifolds and derived categories.
Algebraic Groups
(Zürich : EMS Publ. House, 2007) Jantzen, Jens Carsten; Rouquier, Raphael
The workshop dealt with a broad range of topics from the structure theory and the representation theory of algebraic groups (in the widest sense). There was emphasis on the following areas: structure and classification of wonderful varieties, finite reductive groups and character sheaves, quantum cohomology of homogeneous varieties, representation categories and their connections to orbits and flag varieties.
Algebraic Groups
(Zürich : EMS Publ. House, 2013) Jantzen, Jens Carsten; Reichstein, Zinovy
Linear algebraic groups is an active research area in contemporary mathematics. It has rich connections to algebraic geometry, representation theory, algebraic combinatorics, number theory, algebraic topology, and differential equations. The foundations of this theory were laid by A. Borel, C. Chevalley, T. A. Springer and J. Tits in the second half of the 20th century. The Oberwolfach workshops on algebraic groups, led by Springer and Tits, played an important role in this effort as a forum for researchers, meeting at approximately 3 year intervals since the 1960s. The present workshop continued this tradition, featuring a number of important recent developments in the subject.
Algebraic Groups
(Zürich : EMS Publ. House, 2010) Jantzen, Jens Carsten
The workshop dealt with a broad range of topics from the structure theory and the representation theory of algebraic groups (in the widest sense). There was emphasis on the following areas: • classical and quantum cohomology of homogeneous varieties, • representation theory and its connections to orbits and flag varieties.
Algebraic Groups
(Zürich : EMS Publ. House, 2017) Littelmann, Peter; Reichstein, Zinovy
Linear algebraic groups is an active research area in contemporary mathematics. It has rich connections to algebraic geometry, representation theory, algebraic combinatorics, number theory, algebraic topology, and differential equations. The foundations of this theory were laid by A. Borel, C. Chevalley, J.-P. Serre, T. A. Springer and J. Tits in the second half of the 20th century. The Oberwolfach workshops on algebraic groups, led by Springer and Tits, played an important role in this effort as a forum for researchers, meeting at approximately 3 year intervals since the 1960s. The present workshop continued this tradition, covering a range of topics, with an emphasis on recent developments in the subject.
Algebraic Groups (hybrid meeting)
(Zürich : EMS Publ. House, 2021) Gille, Philippe; Littelmann, Peter
Linear algebraic groups is an active research area in contempo- rary mathematics. It has rich connections to algebraic geometry, representa- tion theory, algebraic combinatorics, number theory, algebraic topology, and differential equations. The foundations of this theory were laid by A. Borel, C. Chevalley, J.-P. Serre, T. A. Springer and J. Tits in the second half of the 20th century. The Oberwolfach workshops on algebraic groups, led by Springer and Tits, played an important role in this effort as a forum for re- searchers, meeting at approximately 3 year intervals since the 1960s. The present workshop continued this tradition, covering a range of topics, with an emphasis on recent developments in the subject.
Algebraic K-Theory
(Zürich : EMS Publ. House, 2006) Huber-Klawitter, Annette; Jannsen, Uwe; Levine, Marc
This is the report on the Oberwolfach workshop Algebraic KTheory, held in July 2006. The talks covered mainly topics from Algebraic Geometry and Number Theory in connection with K-Theory. Special emphasis was placed on motivic cohomology and motivic homotopy of general schemes.
Algebraic K-theory
(Zürich : EMS Publ. House, 2019) Hesselholt, Lars; Huber-Klawitter, Annette; Kerz, Moritz
Algebraic $K$-theory has seen a fruitful development during the last three years. Part of this recent progress was driven by the use of $\infty$-categories and related techniques originally developed in algebraic topology. On the other hand we have seen continuing progress based on motivic homotopy theory which has been an important theme in relation to algebraic $K$-theory for twenty years.