Colloquium: "Quantitative Arithmetic Geometry"

Abstract: Arithmetic geometry is an ancient subject which studies rational solutions on an algebraic variety defined by a system of polynomial equations. One of main questions in arithmetic geometry is the following: How many rational solutions do varieties have? It could be empty or infinite, but if it is infinite, then one can ask how rational solutions are distributed. Are they dense in an appropriate topology? Or one can ask the asymptotic formula for the counting function of rational solutions with respect to an appropriate size function. In this talk, I would like to explain how algebraic geometry is useful to study the last question, asymptotic formulae for the counting function of rational solutions. This is joint work with Brian Lehmann.

Tea @ 3:45 in Cupples I, Room 200

Host: Mohan Kumar