From self-similar groups to self-similar sets and spectra

The survey presents developments in the theory of self-similar groups leading to applications to the study of fractal sets and graphs, and their associated spectra

Automata, Groups, Limit Spaces, and Tilings

We explore the connections between automata, groups, limit spaces of self-similar actions, and tilings. In particular, we show how a group acting ``nicely'' on a tree gives rise to a self-covering of a topological groupoid, and how the group can be reconstructed from the groupoid and its covering. The connection is via finite-state automata. These define decomposition rules, or self-similar tilings, on leaves of the solenoid associated with the covering.Comment: to appear in J. Algebr

Presentations of Topological Full Groups by Generators and Relations

We describe generators and defining relations for the commutator subgroup of topological full groups of minimal subshifts. We show that the word problem in a topological full group is solvable if and only if the language of the underlying subshift is recursive.Comment: Some typos fixe

Plasmon resonance sensitivity in fine metal particle

The sensitivity of the wavelength position of surface plasmon resonances in prolate and oblate fine metal particles to the refractive index of an embedding solution, a particle shape, and electron temperature is studied theoretically in the framework of different analytical methods. All calculations are illustrated on the single potassium nanoparticle as an example.Comment: 3 figures, 6 page