Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (hybrid meeting)
No full textThe first ever MATRIX-MFO tandem workshop addressed several research questions in low-dimensional topology and related areas
Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren
No full textThe Yang–Baxter equation is a fascinating equation that appears in many areas of physics and mathematics and is best represented diagramatically. This snapshot connects the mathematics of braiding hair to the Yang–Baxter equation and relates it to current research about systems of infinite dimensional algebras called "subfactors''
Mini-Workshop: Nonpositively Curved Complexes (online meeting)
No full textThe leading theme of the meeting was to understand nonpositively curved complexes and groups acting on them.
Motivations, questions, results, and techniques being presented and discussed come from various areas of mathematics, including algebraic geometry, Lie groups, metric graph theory, geometric topology, algebraic topology,
coarse geometry, -theory, and, in general, geometric and analytic group theory. The subject discussed focused
around participant's latest achievements, and important open questions in the area
Lifting Spectral Triples to Noncommutative Principal Bundles
No full textGiven a free action of a compact Lie group on a unital C*-algebra and a spectral triple on the corresponding fixed point algebra , we present a systematic and in-depth construction of a
spectral triple on that is build upon the geometry of and . We compare our construction with a selection of established examples
Braid groups, the Yang–Baxter equation, and subfactors
No full textDie Yang–Baxter-Gleichung ist eine faszinierende Gleichung,
die in vielen Gebieten der Physik und der Mathematik
auftritt und die am besten diagrammatisch
dargestellt wird. Dieser Snapshot schlägt einen weiten
Bogen vom Zöpfeflechten über die Yang–Baxter-
Gleichung bis hin zur aktuellen Forschung zu Systemen
von unendlichdimensionalen Algebren, die wir
„Unterfaktoren“ nennen.[Also available in English
Computability Theory (hybrid meeting)
No full textOver the last decade computability theory has seen many new and
fascinating developments that have linked the subject much closer
to other mathematical disciplines inside and outside of logic.
This includes, for instance, work on enumeration degrees that
has revealed deep and surprising relations to general topology,
the work on algorithmic randomness that is closely tied to
symbolic dynamics and geometric measure theory.
Inside logic there are connections to model theory, set theory, effective descriptive
set theory, computable analysis and reverse mathematics.
In some of these cases the bridges to seemingly distant mathematical fields
have yielded completely new proofs or even solutions of open problems
in the respective fields. Thus, over the last decade, computability theory
has formed vibrant and beneficial interactions with other mathematical
fields.
The goal of this workshop was to bring together researchers representing
different aspects of computability theory to discuss recent advances, and to
stimulate future work
Explicit Methods in Number Theory (hybrid meeting)
No full textThe series of Oberwolfach meetings on `Explicit
methods in number theory' brings together people attacking key problems in
number theory via techniques involving concrete or computable descriptions.
Here, number theory is interpreted broadly, including algebraic and analytic
number theory, Galois theory and inverse Galois problems, arithmetic of curves
and higher-dimensional varieties, zeta and -functions and their special
values, modular forms and functions.
The 2021 meeting featured a seven-lecture minicourse on the distribution of
class groups and Selmer groups. The other talks covered a broad range of topics
in number theory ranging, for instance, from deterministic integer factorisation
to the inverse Galois problem, rational points, and integrality of instanton
numbers
Homotopical Algebra and Higher Structures (hybrid meeting)
No full textHomotopical algebra and higher category theory play an increasingly important role in pure mathematics, and higher methods
have seen tremendous development in the last couple of decades. The talks delivered at the workshop described some of the latest progress in this area
and applications to various problems of algebra, geometry, and combinatorics
Finite geometries: pure mathematics close to applications
No full textThe research field of finite geometries investigates structures with a finite number of objects. Classical examples include vector spaces, projective spaces, and affine spaces over finite fields. Although many of these structures are studied for their geometrical importance, they are also of great interest in other, more applied domains of mathematics. In this snapshot, finite vector spaces are introduced. We discuss the geometrical concept of partial t-spreads together with its implications for the “packing problem” and a recent application in the existence of “cooling codes”
Geometric Numerical Integration (hybrid meeting)
No full textThe topics of the workshop
included interactions between geometric numerical integration and numerical partial differential equations;
geometric aspects of stochastic differential equations;
interaction with optimisation and machine learning;
new applications of geometric integration in physics;
problems of discrete geometry, integrability, and algebraic aspects