Benjamin Dozier

Research Focus

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.   

Publications

• Equations of linear subvarieties of strata of differentials (with Frederick Benirschke and Samuel Grushevsky), arXiv:2011.11664 (2020), to appear in Geometry and Topology.
• Measure bound for translation surfaces with short saddle connections, arXiv:2002.10026 (2020).
• Coarse density of subsets of Mg (with Jenya Sapir), arXiv:1908.04458 (2019), to appear in Ann. Inst. Fourier.
• Equidistribution of saddle connections on translation surfaces, J. Mod. Dyn. 14 (2019), 87–120.
• Convergence of Siegel-Veech constants, Geom. Dedicata 198 (2019), 131–142.

Courses - Spring 2023

• MATH 4901 : Supervised Reading
• MATH 7580 : Topics in Topology