Akshay Venkatesh (Stanford University) will present the Trjitzinsky Memorial Lectures. Lecture II. The topology of arithmetic manifolds. I will discuss the topology of arithmetic hyperbolic 3-manifolds ( but only after explaining what these are!), emphasizing features which seem to differ from the typical behavior of hyperbolic 3-manifolds, and finally how these features seem to be related to deep Diophantine problems like the ABC conjecture.