Boris Solomyak
Professor, appointed 1992 (Ph.D. Leningrad University 1986)
Research area: Fractals and dynamics
Personal Web page: http://www.math.washington.edu/~solomyak/personal.html
E-mail: solomyak[_a_t_]math.washington.edu
Phone: 685-1307
Office: PDL C-328
Courses taught this quarter: MATH 126 D & 524 A
Hobbies: Hiking, cross-country skiing, art history
Professional interests
My research interests include fractal geometry and dynamical systems. I am studying them from a theoretical point of view, although some of the work I am doing has connections to physics. In particular, I am interested in the Hausdorff dimension and topological properties of self-similar sets. I investigated Bernoulli convolutions and arithmetic sums of Cantor sets. The study of fractals involves geometric measure theory and harmonic analysis.
In dynamics, I am interested in substitutions and tiling systems, especially
in their spectral properties. Tilings (such as the Penrose tiling) are used as
models of quasicrystals. Roughly speaking, quasicrystals are solids with a
diffraction pattern typical for crystals, but which is incompatible with a
periodic structure.
Selected bibliography
Fractals in the plane with positive length and zero Buffon needle probability
(with Y. Peres and K. Simon), American Mathematical Monthly 110
(2003), 314--325.
Consequences of pure point diffraction spectra for multiset substitution systems
(with J.-Y. Lee and R. V. Moody), Discrete and Computational Geometry
29 (2003), 525--560.
Spectra of Bernoulli convolutions as multipliers in L p
on the circle (with N. Sidorov), Duke Math. Journal 120 (2003),
353--370.
Dynamics of self-similar tilings, Ergodic Theory and Dynamical Systems
17 (1997), 695--738.
On the random series ∑± λn (an Erdös
problem), Annals of Math. 142 (1995), 611--625.
Finite beta-expansions (with C. Frougny), Ergodic Theory and Dynamical
Systems 12 (1992), 713--723.