UIC Graduate Student Seminar

Friday October 12
3:00 pm
636 SEO

Speaker: Henri Gillet

Title: Counting solutions of equations in more than three variables Conjectures of Lang and Vojta, also some conjectures of Manin and others.

Abstract: Once the Mordell Conjecture has been proved, it is natural to ask about polynomial equations in more variables.

One question is which equations have "few" solutions. Serge Lang made a conjecture, generalizing the Mordell conjecture, which is still open. I shall give some idea of what this conjecture says, and discuss the Vojta conjectures - which link these questions with Nevanlinna theory - an area in complex analysis.

Finally, I will try to say something about the work of Yuri Tschinkel and others about equations with "many" solutions.