## 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.