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Benjamin Dozier
Assistant Professor
Departments/Programs
- Mathematics
Research
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.
Courses
Spring 2022
Fall 2022
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.