Lecture Page

        This page contains pdf files for various lectures that I've given.
  Selmer groups and congruences, A 45 minute lecture presented in the Number Theory Section at the ICM in Hyderabad, India, August, 2010.
  Iwasawa theory and projective modules, A lecture given at the conference on Galois Representations in Arithmetic and Geometry which took place in Goa, India, August, 2010.
  Galois representations with open image, My lecture at the Pacific Northwest Number Theory Conference which took place in Bellingham, Washington, May, 2011.
  The derivative formula for Kubota-Leopoldt p-adic L-functions at trivial zeros, My lecture at p-adic Modular Forms and Arithmetic, a conference in honor of Haruzo Hida's 60th birthday at UCLA in June, 2012.