Anthony Várilly-Alvarado's research interests lie at the interface of algebraic geometry and number theory.  He studies the fundamental arithmetic properties of solutions to systems of polynomial equations in several variables, especially those systems whose geometric avatars are four-dimensional spaces.  Before joining Rice, Várilly-Alvarado received an A.B. in Mathematics from Harvard University, he completed Part III of the Mathematical Tripos at the University of Cambridge, and obtained a Ph. D. in Mathematics from UC Berkeley.  He has taught a variety of courses, ranging from introductory courses like Single Variable Calculus and Honors Linear Algebra through to advanced graduate courses on Elliptic Curves and Algebraic Surfaces.