[math-fun] Penrose Tilings/Algebraic Number Theory

This young fellow is looking to spend more time in the U.S. due to a romantic interest. Does anyone here have any suggestions about places he might start looking ? "I have a B.S in mathematics and computer science. My bachelor thesis was on algebraic aspects of Penrose Tilings. My upcoming thesis is in the field of Algebraic Number Theory, more specifically in the theory of valuations and Galois representations, even more specifically the higher ramification groups and The Artin Conductor."