Spectral Structures and Topological Methods in Mathematics [electronic resource] / Michael Baake, Friedrich Götze, Werner Hoffmann

Format:

Book

Author/Creator:

Baake, Michael, editor.

Contributor:

Götze, Friedrich,;, editor.

Hoffmann, Werner, editor.

Series:

Series of congress reports

EMS Series of Congress Reports (ECR) ; 2523-515X

Language:

English

Subjects (All):

Topology.

Mathematical analysis.

Information visualization.

Mathematics and science.

Calculus & mathematical analysis.

Physical Description:

1 online resource (433 pages)

Place of Publication:

Zuerich, Switzerland : European Mathematical Society Publishing House, 2019

Zürich, Switzerland : European Mathematical Society, 2019.

Language Note:

English

System Details:

text file PDF

Summary:

This book is a collection of survey articles about spectral structures and the application of topological methods bridging different mathematical disciplines, from pure to applied. The topics are based on work done in the Collaborative Research Centre (SFB) 701. Notable examples are non-crossing partitions, which connect representation theory, braid groups, non-commutative probability as well as spectral distributions of random matrices. The local distributions of such spectra are universal, also representing the local distribution of zeros of $L$-functions in number theory. An overarching method is the use of zeta functions in the asymptotic counting of sublattices, group representations etc. Further examples connecting probability, analysis, dynamical systems and geometry are generating operators of deterministic or stochastic processes, stochastic differential equations, and fractals, relating them to the local geometry of such spaces and the convergence to stable and semi-stable states.

Contents:

Convergence and asymptotic approximations to universal distributions in probability /; Friedrich Götze, Holger Kösters

; Kolmogorov operators and SPDEs /; Michael Röckner

; Analysis and stochastic processes on metric measure spaces /; Alexander Grigor'yan

; Markov evolutions in spatial ecology: From microscopic dynamics to kinetics /; Yuri Kondratiev, Oleksandr Kutoviy, Pavlo Tkachov

; Metastability in randomly perturbed dynamical systems: Beyond large-deviation theory /; Barbara Gentz

; Computation and stability of waves in equivariant evolution equations /; Wolf-Jürgen Beyn, Denny Otten

; Initial value problems for nonlinear dispersive equations at critical regularity /; Sebastian Herr

; Variational solutions to nonlocal problems /; Moritz Kassmann

; Spectral and arithmetic structures in aperiodic order /; Michael Baake, Franz Gähler, Christian Huck, Peter Zeiner

; Affine special Kähler structures in real dimension two /; Martin Callies, Andriy Haydys

; Non-crossing partitions /; Barbara Baumeister, Kai-Uwe Bux, Friedrich Götze, Dawid Kielak, Henning Krause

; The derived category of the projective line /; Henning Krause, Greg Stevenson

; Higher finiteness properties of braided groups /; Kai-Uwe Bux

; Zeta functions and the trace formula /; Werner Hoffmann

; Zeta functions of groups and rings - functional equations and analytic uniformity /; Christopher Voll

; Conjectures of Brumer, Gross and Stark /; Andreas Nickel

; Displays and $p$-divisible groups /; Thomas Zink.

ISBN:

3-03719-697-1