Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
Not a member yet
2063 research outputs found
Sort by
Searching for the monster in the trees
No full textThe Monster finite simple group is almost unimaginably large, with about 8 × 1053 elements in it. Trying to understand such an immense object requires both theory and computer programs. In this snapshot, we discuss finite groups, representations, and finally Brauer trees, which offer some new understanding of this vast and intricate structure
Deterministic Dynamics and Randomness in PDE
No full textOver the last few years there has been spectacular progress in the study of parabolic SPDE, of nonlinear dispersive and wave equations and of probabilistic methods in PDE.
An important direction connecting these three fields is the general question of how randomness affects the behavior of solutions to PDE.
Research in recent years has been driven by the study of randomness in nonlinear evolution equations with a focus on the question of how to quantify the transport of such randomness under the nonlinear flow
Arbeitsgemeinschaft: Higher Rank Teichmüller Theory
No full textHigher rank Teichmüller theory is the study of certain connected components of character varieties of surface groups in higher rank semisimple Lie groups, with the property that all elements in these components correspond to faithful representations with discrete image. Like classical Teichmüller theory, this relatively recent theory is very rich and builds on a combination of methods from various areas of mathematics. Its many facets were explored in detail during the Arbeitsgemeinschaft
Algebraic K-Theory
No full textAlgebraic -theory has seen further progress during the
last three years. One important aspect of this recent progress
has been a better conceptual understanding of motivic filtrations on -theory and the
systematic use of localizing invariants and related concepts. Progress on motivic cohomology has also played an
important role concerning foundations as well as applications
Mini-Workshop: Topological and Differential Expansions of o-minimal Structures
No full textThe workshop brought together researchers with expertise in areas of mathematics where model theory has had interesting applications. The areas of expertise spanned from expansions of o-minimal structures preserving tame geometric properties to expansions of specified fields by classical operators that preserve neo-stability properties. There were presentations and discussions on recent developments in definable groups and decompositions in relatively tame setups, the interplay of different notions of dimension and closure operators, and applications of the model theory of differential fields to diophantine geometry
Applications of Nijenhuis Geometry III: Frobenius Pencils and Compatible Non-Homogeneous Poisson Structures
No full textWe consider multicomponent local Poisson structures of the form , under the assumption that the third order term is Darboux-Poisson and non-degenerate, and study the Poisson compatibility of two such structures. We give an algebraic interpretation of this problem in terms of Frobenius algebras and reduce it to classification of Frobenius pencils, i.e. of linear families of Frobenius algebras. Then, we completely describe and classify Frobenius pencils under minor genericity conditions. In particular we show that each such Frobenuis pencil is a subpencil of a certain pencil. These maximal pencils are uniquely determined by some combinatorial object, a directed rooted in-forest with vertices labeled by natural numbers whose sum is the dimension of the manifold. These pencils are naturally related to certain (polynomial, in the most nondegenerate case) pencils of Nijenhuis operators. We show that common Frobenius coordinate
systems admit an elegant invariant description in terms of the Nijenhuis pencil
History of Mathematics through Collaboration: Toward a Composite Portrait of Oswald Veblen
No full textOswald Veblen played a pivotal role in the history of American mathematics in the twentieth century. His life, however, remains largely unstudied. This conference was designed to redress this issue by exploring Oswald Veblen and his contributions to the history of American and international mathematics in an interactive workshop that used the Veblen Papers from the US Library of Congress as a foundational and shared resource. With this frame, the conference raised queries and discussed issues related to Veblen, his mathematical contributions, and his collaborative initiatives, including his critical work aiding refugee mathematicians in WWII that helped establish long standing programs at American institutions that continue to advance mathematics at the highest level. The workshop echoed Veblen's collaborative focus and brought together historians of mathematics and mathematicians to work alongside one another during the conference. This content and collaborative approach combined to advance our understanding of Veblen's collaborations and the history of twentieth-century mathematics more broadly
Route planning for bacteria
No full textBacteria have been fascinating biologists since their discovery in the late 17th century. By analysing their movements, mathematical models have been developed as a tool to understand their behaviour. However, adapting these models to real situations can be challenging, because the model coefficients cannot be observed directly. In this snapshot, we study this question mathematically and explain how the idea of “route planning” can be used to determine these model coefficients
Calculus of Variations
No full textThe Calculus of Variations is at the same time a classical
subject, with long-standing open questions which have
generated exciting discoveries in recent decades, and a modern subject
in which new types of questions arise, driven
by mathematical developments and emergent applications.
It is also a subject with a very wide scope, touching on
interrelated areas that include geometric variational problems, optimal transportation,
geometric inequalities and domain optimization
problems, elliptic regularity, geometric measure theory,
harmonic analysis, physics, free boundary problems, etc.
The workshop balances the traditional interests of past conferences with new emerging
perspectives
Groups and Dynamics: Topology, Measure, and Borel Structure
No full textWhile the subjects of topological dynamics, ergodic theory, and descriptive set theory
have long interacted in a variety of profitable ways,
recent developments have ushered in a vigorous new phase of
interplay between them, from the abstract transfer and coordinated development of ideas
and methods (as in the theory of dynamical tilings)
to the direct leveraging of technical points of contact (as in boundary theory). The workshop
served as a platform for promoting and advancing these connections by bringing together
researchers working on various facets of topological, measured, and Borel dynamics