| Title |
Spectral Structures and Topological Methods in Mathematics ([EBook] /) / Michael Baake, Friedrich Götze, Werner Hoffmann |
| Added Personal Name |
Baake, Michael |
| Götze, Friedrich |
| Hoffmann, Werner |
| Publication |
Zuerich, Switzerland : : European Mathematical Society Publishing House, , 2019 |
| Physical Details |
1 online resource (433 pages) |
| Series |
EMS Series of Congress Reports (ECR) 2523-515X |
| ISBN |
9783037196977 |
| Summary Note |
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 note |
Convergence and asymptotic approximations to universal distributions in probability /: Kolmogorov operators and SPDEs /: Analysis and stochastic processes on metric measure spaces /: Markov evolutions in spatial ecology: From microscopic dynamics to kinetics /: Metastability in randomly perturbed dynamical systems: Beyond large-deviation theory /: Computation and stability of waves in equivariant evolution equations /: Initial value problems for nonlinear dispersive equations at critical regularity /: Variational solutions to nonlocal problems /: Spectral and arithmetic structures in aperiodic order /: Affine special Kähler structures in real dimension two /: Non-crossing partitions /: The derived category of the projective line /: Higher finiteness properties of braided groups /: Zeta functions and the trace formula /: Zeta functions of groups and rings – functional equations and analytic uniformity /: Conjectures of Brumer, Gross and Stark /: Displays and $p$-divisible groups /: |
| Mode of acces to digital resource |
Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
https://doi.org/10.4171/197 |
| See Also |
https://www.ems-ph.org/img/books/baake_mini.jpg |
| Links to Related Works |
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