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.