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Horizons of fractal geometry and complex dimensions. 2016 summer school on fractal geometry and complex dimensions, in celebration of the 60th birthday of Michel Lapidus, California Polytechnic State University, San Luis Obispo, California, USA, June 21–29, 2016. (English) Zbl 1420.00047

Contemporary Mathematics 731. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-3581-3/pbk; 978-1-4704-5315-2/ebook). xiv, 302 p. (2019).

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Publisher’s description: This volume contains the proceedings of the 2016 Summer School on Fractal Geometry and Complex Dimensions, in celebration of Michel L. Lapidus’s 60th birthday, held from June 21–29, 2016, at California Polytechnic State University, San Luis Obispo, California.
The theme of the contributions is fractals and dynamics and content is split into four parts, centered around the following themes: Dimension gaps and the mass transfer principle, fractal strings and complex dimensions, Laplacians on fractal domains and SDEs with fractal noise, and aperiodic order (Delone sets and tilings).
The articles of this volume will be reviewed individually.
Indexed articles:
Allen, Demi; Troscheit, Sascha, The mass transference principle: ten years on, 1-33 [Zbl 1423.11124]
Baake, Michael; Haynes, Alan, A measure-theoretic result for approximation by Delone sets, 35-40 [Zbl 1423.11128]
Barnsley, M. F.; Vince, A., Self-similar tilings of fractal blow-ups, 41-62 [Zbl 1427.52014]
Eichinger, Tobias; Winter, Steffen, Regularly varying functions, generalized contents, and the spectrum of fractal strings, 63-94 [Zbl 1423.35282]
Falk, Kurt, Dimensions of limit sets of Kleinian groups, 95-114 [Zbl 1428.30048]
van Frankenhuijsen, Machiel, The spectral operator and resonances, 115-131 [Zbl 1423.11149]
Kesseböhmer, M.; Samuel, T.; Weyer, Hendrik, Measure-geometric Laplacians for discrete distributions, 133-142 [Zbl 1423.35284]
Lapidus, Michel L., An overview of complex fractal dimensions: from fractal strings to fractal drums, and back, 143-265 [Zbl 1423.28023]
Pollack, Paul; Pomerance, Carl, Eigenvalues of the Laplacian on domains with fractal boundary, 267-277 [Zbl 1427.58013]
Zähle, Martina; Schneider, Erik, Forward integrals and SDE with fractal noise, 279-302 [Zbl 1423.60086]

MSC:

00B25 Proceedings of conferences of miscellaneous specific interest
28-06 Proceedings, conferences, collections, etc. pertaining to measure and integration
37-06 Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory
00B30 Festschriften
11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses
26A30 Singular functions, Cantor functions, functions with other special properties
28D05 Measure-preserving transformations
30D10 Representations of entire functions of one complex variable by series and integrals
31A10 Integral representations, integral operators, integral equations methods in two dimensions
35P20 Asymptotic distributions of eigenvalues in context of PDEs
37B10 Symbolic dynamics
52A39 Mixed volumes and related topics in convex geometry
52C23 Quasicrystals and aperiodic tilings in discrete geometry
60G50 Sums of independent random variables; random walks

Biographic References:

Lapidus, Michel
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