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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.
- 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.