Rob Benedetto
Amherst College

The abc Conjecture: An Introduction

The abc conjecture is a straightforward statement about the prime factors of integers a, b, and c satisfying the equation a+b=c. In spite of the simple name, simple equation, and simple statement, however, the conjecture appears to be very difficult. Many mathematicians consider it to be one of the most important open problems in number theory.

In this talk, we will motivate and state the abc conjecture. To help us along, we'll look at the related case of putting polynomials, rather than integers, in the roles of a, b, and c. We'll also present some potential applications to other problems in number theory, and we'll present some of the evidence supporting the conjecture.

Bio

Rob Benedetto received his Ph.D. at Brown University, where he studied Number Theory under Joe Silverman. He spent two years as a visiting professor at the University of Rochester, followed by two years as an NSF-sponsored research postdoc at Boston University. Since 2002, he has held the position of assistant professor at Amherst College.

Awards
NSF Grant, Amherst College, 2006-2009.
Trustee Faculty Fellowship, Amherst College, 2005-2006.
NSA Young Investigator's Grant, Amherst College, 2004-2006.
Miner D. Crary Summer Research Fellowship, Amherst College, 2004.
NSF Mathematical Sciences Research Postdoc, 2000.
Nominated for Professor of the Year, University of Rochester, 2000.
Nominated for Professor of the Year, University of Rochester, 1999.
R.B. Lindsay Graduate Research Fellowship, Brown University, 1997-98.
Mathematics Department Outstanding Teaching Prize, Brown University, 1997.