**Ravi Ramakrishna**

Cornell University, Ithaca

February 27, 2014

**Galois Representations**:
In the last 30 years representations of (infinite) Galois groups have
played an increasingly important role in number theory. Indeed, arithmetic objects such as the Diophantine equation $y=x^3-x^2+1$ or $x^n+y^n=z^n$ often have attached Galois representations that `know' the solutions. This talk will survey a small slice of this theory and will be accessible to mathematicians in all disciplines.