A quick introduction to Dwork's conjecture

Abstract

This is an expository paper which gives a quick introduction to Dwork's conjecture about p-adic meromorphic continuation of his unit root zeta function arising from algebraic geometry. Special emphasis is given to the case of elliptic family and its relation to p-adic modular forms such as Gouvêa-Mazur conjecture and some sort of p-adic Ramanujuan-Peterson conjecture. There is also a section describing some of my personal interactions with Dwork.