Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Holonomy Groups of -Manifolds
No full textMSC classes: 2010: 53C29 53C50 53C10Research in Pairs 2016We classify the holonomy algebras of manifolds admitting an indecomposable torsion free -structure, i.e. for which the holonomy representation does not leave invariant any proper non-degenerate subspace. We realize some of these Lie algebras as holonomy algebras of left-invariant metrics on Lie groups
Interplay between Number Theory and Analysis for Dirichlet Series
No full textIn recent years a number of challenging research problems have crystallized in the analytic theory of Dirichlet series and its interaction with function theory in polydiscs. Their solutions appear to require unconventional combinations of expertise from harmonic, functional, and complex analysis, and especially from analytic number theory. This MFO workshop provided an ideal arena for the exchange of ideas needed to nurture further progress and to solve important problems
Aperiodic Order and Spectral Properties
No full textPeriodic structures like a typical tiled kitchen floor
or the arrangement of carbon atoms in a diamond
crystal certainly possess a high degree of order. But
what is order without periodicity? In this snapshot,
we are going to explore highly ordered structures that
are substantially nonperiodic, or aperiodic. As we
construct such structures, we will discover surprising
connections to various branches of mathematics, materials
science, and physics. Let us catch a glimpse
into the inherent beauty of aperiodic order
Mini-Workshop: MASAs and Automorphisms of C*-Algebras
No full textThe main aim of this workshop was to study maximal abelian *-subalgebras of C*-algebras from various points of view. A chief motivation is the UCT problem, which asks whether all separable nuclear C*-algebras satisfy the universal coefficient theorem of Rosenberg and Schochet. The connection, in terms of existence of invariant Cartan MASAs for certain *-automorphisms of the Cuntz algebra, has been brought up only very recently; it opens up a line of new perspectives on pressing questions in the structure and classification theory of simple nuclear C*-algebras and their automorphism groups, which has made giant leaps forward in the past five years. Connections to other areas, in particular von Neumann algebras and coarse geometry, have been explored as well
Mathematical Questions and Challenges in Quantum Electrodynamics and its Applications
No full textQuantum field theory (QFT) may be considered one of the most fundamental frameworks of theoretical physics. Quantum Electrodynamics (QED) is the part of QFT that describes the interaction between matter and light. Although it is one of the experimentally best tested theories, it yet faces many open mathematical questions and challenges. The mathematical rigorous framework of QED and the implications deriving from it is the topic of Workshop 1737 held at MFO from September 11 through 15, 2017, bringing together mathematicians and theoretical physicists to discuss topics such as high- and low-energy QED, external field QED, quantum optics, many-boson and many-fermion systems, transport properties in condensed matter
Linear Syzygies, Hyperbolic Coxeter Groups and Regularity
No full textMSC: 13F55; 20F55; 13D02Research in Pairs 2015We build a new bridge between geometric group theory and commutative algebra by showing that the virtual cohomological dimension of a Coxeter group is essentially the regularity of the Stanley–Reisner ring of its nerve. Using this connection and techniques from the theory of hyperbolic Coxeter groups, we study the behavior of the Castelnuovo–Mumford regularity of square-free quadratic monomial ideals. We construct examples of such ideals which exhibit arbitrarily high regularity after linear syzygies for arbitrarily many steps. We give a doubly logarithmic bound on the regularity as a function of the number of variables if these ideals are Cohen–Macaulay
Harmonic Analysis and the Trace Formula
No full textThe purpose of this workshop was to discuss recent results in harmonic analysis that arise in the study of the trace formula. This theme is common to different directions of research on automorphic forms such as representation theory, periods, and families
Reducing sub-modules of the Bergman module under the action of the symmetric group
No full textMSC: 47A13; 47B32; 20B30OWLF 2017The weighted Bergman spaces on the polydisc, , splits into orthogonal direct sum of subspaces indexed by the partitions of which are in one to one correspondence with the equivalence classes of the irreducible representations of the symmetric group on symbols. In this paper, we prove that each sub-module is a locally free Hilbert module of rank equal to square of the dimension of the corresponding irreducible representation. It is shown that given two partitions and , if then the sub-modules and are not equivalent. We prove that for the trivial and the sign representation corresponding to the partitions and , respectively, the sub-modules and are inequivalent. In particular, for , we show that all the sub-modules in this decomposition are inequivalent
Espacios de métricas Riemannianas
No full textRiemannian metrics endow smooth manifolds such as
surfaces with intrinsic geometric properties, for example
with curvature. They also allow us to measure
quantities like distances, angles and volumes. These
are the notions we use to characterize the "shape" of
a manifold. The space of Riemannian metrics is a
mathematical object that encodes the many possible
ways in which we can geometrically deform the shape
of a manifold.[Also available in Spanish