Boris Solomyak's Research Interests

My main interests are fractals and dynamical systems. During the last 8 year I have worked on the following topics:

Iterated function systems (linear and non-linear hyperbolic and parabolic), self-similar and self-affine sets, Hausdorff dimension, Cantor sets and measures, Bernoulli convolutions, self-similar tilings, tiling dynamical systems, spectral theory of tilings and substitutions, adic transformations, beta-expansions, zeros of power series with restricted coefficients, numeration systems related to Pisot-Vijayaraghavan numbers.

I obtained my Ph.D. in 1986 at the St.Petersburg (formerly Leningrad) State University, in the area of operator theory and functional analysis.

non-commutative algebraic geometry. Commutative algebra and algebraic geometry are inextricably linked, and each subject supports the other. One may take either the algebraic or geometric point of view as the fundamental one, depending on taste, or the issue under consideration. However, until quite recently there was no geometric point of view on non-commutative rings. Adopting a geometric perspective leads to a view of non-commutative algebra which is new and fruitful. I believe that ultimately the geometric perspective will be dominant.