Friday, November 21, 2014 4:00 pm
-
4:00 pm
EST (GMT -05:00)
Xiaoheng Jerry Wang, Princeton University
“Rational points on hyperelliptic curves”
Finding integral and rational solutions to polynomial equations with integer coefficients has always been a fascinating subject to mathematicians. In this talk we will look at the hyperelliptic equations y2 = f(x) and discuss how many solutions they have in general, and how many solutions they have typically. The first question has a nice answer in terms of a topological invariant, the genus, of the curve. There has been several results on the second question recently by Manjul Bhargava and his collaborators. We will discuss our recent join work with Manjul Bhargava and Benedict Gross on solutions to the hyperelliptic equations over odd degree field extensions of Q and see how the geometry of pencils of quadrics plays a pivotal role in this work.Refreshments will be served in MC 5158B at 3:30 p.m. Everyone is welcome to attend.