Problems for the seminar, ICTP, 2007-2008

The following problems for the ICPT seminar 2007-2008 are specified: topological classification of polynomials; equipartition of indivisible integer vectors; geometrical progressions? fractional parts? equipartitions; statistics of continued fractions of eigenvalues of matrices; growth rate of elements of periodic continued fractions; periods of geometrical progressions of residues; Kolmogorov?s distributions; stochasticity degree of arithmetical progressions of fractional parts; is a generic geometrical progression of fractional parts random?; prime numbers distribution?s randomness; algorithmic unsolvability of problems of higher dimensional continued fractions; periods of continued fractions of roots of quadratic equations; statistics of lengths of periods of continued fractions of quadratic irrational numbers; random matrices? characteristic polynomials distributions.