Joseph H. Silverman

An abstract discrete dynamical system consists of a set X and a self-map f from X to itself. Dynamics studies the orbits of points of X under repeated application of f. When X and f are defined by polynomials, algebraic geometry comes into play, and...

Secure online communications and financial transactions depend on public key cryptography—but the methods we use today are susceptible to attack by quantum computers. When that will happen is uncertain, though estimates range from 5 to 25 years. This...