Rational Solutions to Cubic Equations

Beginning with some simple principles that go back to the ancient Greeks for solving some low-degree equations, we will then turn to some basic questions raised by Euler and Fermat, whose answers have led to surprising applications (secure Internet commerce) as well as to the solution of famous conjectures (Fermat's Last Theorem). This will bring us to some fundamental problems that remain unsolved to this day. 

You can learn more about Benedict Gross at http://www.math.harvard.edu/~gross/