UIC Graduate Student Seminar
Friday October 12
Speaker: Henri Gillet
Title: Counting solutions of equations in more than three variables Conjectures of Lang and Vojta, also some conjectures of Manin and
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.