Wentang Kuo, Department of Pure Mathematics, University of Waterloo
"Number Theory in Function Fields"
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Integers can be considered either in themselves, such as properties of prime numbers, or as solutions to equations. The quotient field of the ring of polynomials is called the rational function field. As the ring of polynomials over a finite field shares similar arithmetic properties to the ring of integers, many problems in integers have analogues for polynomials. In this talk, we will use Fermat's last theorem and the prime number theorem as examples to discuss their analogues in polynomials. Also, in spite of similarities between rational numbers and the rational function field, we will talk about differences and difficulties arising from problems in these two settings.
MC 5403