Abstract: The filled Julia set of a complex polynomial P is the set of points whose orbit under iteration of the map P is bounded. William Thurston asked "What are the possible shapes

Abstract: Arithmetic geometry is an ancient subject which studies rational solutions on an algebraic variety defined by a system of polynomial equations.

Abstract: A dynamical system, such as a flow or transformation, is called hyperbolic if it tends to stretch and contract the underlying space in different directions.

Abstract: We will discuss the problem of covering a compact set by a minimal number of balls of the given radius. This problem is known to be somewhat dual to the famous best-packing problem.

Abstract: Statistical inference along with the strategy of divide-and-combine for Big Data analysis has been little studied. As an effective inferential tool,

Abstract: Let V be a linear subspace of M_n(C) which contains the identity matrix and is stable under the formation of Hermitian adjoints. I claim that if n is sufficiently large then there exists