Dynamical Systems and Applications

June 19 - June 30

TIME: MR 12:45 pm - 2:45 pm

INSTRUCTOR: MARK LEVI

The lectures will focus on selected research topics, providing the necessary theoretical background for research projects. We will touch on the following subjects: billiards; dynamics of rigid bodies and gyroscopes; resonances and their topology; circle mappings and applications to forced oscillators.

The Prime Numbers and Their Properties

July 3 - July 14

TIME: MR 9:35 am - 11:35 am

INSTRUCTOR: ROBERT VAUGHAN

Many of the most important fundamental unsolved problems in mathematics today concern prime numbers. We will examine some of the properties of prime numbes and develop the basic underlying theories. Particular emphasis will be laid on distributional questions, and some of the topics to be included are Chebychev's inequalities and Merten's theory together with some of the relevant theory of arithemtical functions, and special cases of Dirichlet's theorem on primes in arightmetic progression. There will also be some discussion of connections with the theory of Dirichlet series, and the Riemann Hypothesis, probably the single most important unsolved problem in mathematics today.