Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Automorphic Forms and Arithmetic (hybrid meeting)
No full textThe workshop was at the interface of automorphic forms and analytic number theory. The aim was to disseminate, discuss and develop important new methods and results in the analytic theory of automorphic forms, in particular on higher rank groups, as well as their arithmetic applications. This includes, for instance, the study of various aspects of -functions such as moments, reciprocity laws, and probabilistic aspects, counting problems with automorphic forms, applications of results of algebraic geometry to automorphic forms, as well as analytic aspects of automorphic forms over function fields
Non-Commutative Geometry and Cyclic Homology (hybrid meeting)
No full textThe workshop on "Non-Commutative Geometry and Cyclic Homology" was attended by 16 participants on site. 30 participants could not travel to Oberwolfach because of the pandemia and took advantage of the videoconference tool. This report contains the extended abstracts of the lectures both given on site and externally
Braidoids
No full textBraidoids generalize the classical braids and form a counterpart theory to the theory of planar knotoids, just as the theory of braids does for the theory of knots. In this paper, we introduce the notion of braidoids in , a closure operation for braidoids, we prove an analogue of the Alexander theorem, namely an algorithm that turns a knotoid into a braidoid, and we formulate and prove a geometric analogue of the Markov theorem for braidoids using the -moves
Mini-Workshop: Computational Optimization on Manifolds (online meeting)
No full textThe goal of the mini-workshop was to study the geometry, algorithms and applications of unconstrained and constrained optimization problems posed on Riemannian manifolds.
Focus topics included the geometry of particular manifolds, the formulation and analysis of a number of application problems, as well as novel algorithms and their implementation
History of Mathematics: A Global Cultural Approach (online meeting)
No full textThe primary purpose of this workshop was to take account of progress on an ongoing six-volume cultural history of mathematics from antiquity to the present. This project is led by nine editors working with a large team of authors. Since the workshop had to be held remotely, it took the form of various group meetings held throughout the week. The final session involved assessments by editors of the six volumes with an eye toward completing the project by the end of 2021. The abstracts below summarize the contents of the individual chapters in the entire project, which will be published in Bloomsbury's cultural history series
Unexpected Properties of the Klein Configuration of 60 Points in
No full textFelix Klein in course of his study of the regular and its symmetries encountered a highly symmetric configuration of 60 points in . This configuration has appeared in various guises, perhaps post notably as the configuration of points dual to the 60 reflection planes in the group in the Shephard-Todd list.
In the present note we show that the 60 points exhibit interesting properties relevant from the point of view of two paths of research initiated recently. Firstly, they give rise to two completely different unexpected surfaces of degree 6. Unexpected hypersurfaces have been introduced by Cook II, Harbourne, Migliore, Nagel in 2018. One of unexpected surfaces associated to the configuration of 60 points is a cone with a single singularity of multiplicity 6 and the other has three singular points of multiplicities 4; 2 and 2. Secondly, Chiantini and Migliore observed in 2020 that there are non-trivial sets of points in with the surprising property that their general projection to is a complete intersection. They found a family of such sets, which they called grids. An appendix to their paper describes an exotic configuration of 24 points in which is not a grid but has the remarkable property that its general projection is a complete intersection. We show that the Klein configuration is also not a grid and it projects to a complete intersections. We identify also its proper subsets, which enjoy the same property
Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory
No full textThe Kronecker, plethysm and Sylow branching coefficients describe the decomposition of representations of symmetric groups obtained by tensor products and induction.
Understanding these decompositions has been hailed as
one of the definitive open problems in algebraic combinatorics and has profound and deep connections with representation theory, symplectic geometry, complexity theory, quantum information theory, and local-global conjectures in representation theory of finite groups.
The overarching theme of the Mini-Workshop has been the use of hidden, richer representation theoretic structures to
prove and disprove conjectures concerning these coefficients.
These structures arise from
the
modular and local-global representation theory of symmetric groups,
graded representation theory of Hecke and Cherednik algebras, and categorical Lie theory
Set Theory (online meeting)
No full textSet theory continues to experience dramatic progress, both in pure
set theory, with its fundamental techniques of forcing, large cardinals, and inner
model theory, and in applied set theory, with its deep connections to other areas
of mathematics. Specific topics include: (Pure Set Theory) Forcing axioms,
iteration theorems for various classes of forcings, cardinal characteristics and
descriptive set theory of the continuum and of generalized Baire spaces, HOD
(the hereditarily ordinal definable sets), inner model theory and the core model
induction, singular cardinal combinatorics and cardinal arithmetic (pcf theory),
partition theorems, Borel reducibility; (Applied Set Theory) Borel and measurable
combinatorics, structural Ramsey theory, set theory and operator algebras,
topological dynamics and ergodic theory, set theory and Banach spaces, metric
structures