|Date: Wednesday, November 29, 2017
Location: 3866 East Hall (3:00 PM to 4:00 PM)
Title: Function field analogies, the ABC conjecture, and the ABC theorem
Abstract: The ABC conjecture is an elementary but far-reaching statement in number theory, whose status as a conjecture is currently disputed, but which is in any case extremely difficult. However, when we consider the corresponding statement about polynomials rather than integers (and more generally, about function fields rather than number fields) it has an accessible proof.
In this talk, I'll first explain the basic similarities between number fields and function fields, and present the two associated versions of the ABC conjecture. Then I'll show how the function field case allows us to draw on tools of algebraic geometry (specfically, the Riemann-Hurwitz formula) to turn the conjecture into a theorem.
Speaker: Will Dana