Benjamin Dozier

Dynamical systems, Riemann surfaces

I primarily study translation surfaces and Riemann surfaces, and their moduli spaces.  A central theme is the rich interplay between concrete problems concerning dynamics on individual surfaces and more abstract questions about moduli spaces.   Recently I have used various compactifications of these moduli spaces.  My work has connections to algebraic geometry, hyperbolic geometry, homogeneous dynamics, ergodic theory, geometry of numbers, and probability theory.