Seminar

Location:  60 Evans Hall- UC Berkeley

Speaker: Melanie Matchett Wood (American Institute of Mathematics and Stanford University)

Title: Counting Points on Curves over Finite Fields

Abstract: A curve is a one dimensional space cut out by polynomial
equations, such as y2=x3+x.  In particular, one can consider curves
over finite fields, which means the polynomial equations should have
coefficients in some finite field and that points on the curve are
given by values of the variables (x and y in the example) in the
finite field that satisfy the given polynomials.  A basic question is
how many points such a curve has, and for a family of curves one can
study the distribution of this statistic.  We will give concrete
examples of families in which this distribution is known or predicted,
and give a sense of the different kinds of mathematics that are used
to study different families.