# Spectral Structures and Topological Methods in Mathematics

Share this page *Edited by *
*Michael Baake; Friedrich Götze; Werner Hoffmann*

A publication of the European Mathematical Society

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 and also represent 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.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Specialists working in both pure and applied mathematics.