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# Mathematics Colloquium: Arithmetic Statistics: Points On Curves Over Finite Fields

2017-10-05

Neill 5W, 4:10pm

Alina Bucur

A curve is a one dimensional space cut out by polynomial equations. 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 in the finite field that satisfy the given polynomials. A basic question is how many points such a curve has, and fora 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. Refreshments served at 3:30 p.m. Hacker Lounge (Neill 216)