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Benjamin Dozier

Assistant Professor

Malott Hall, Room 582
bed47@cornell.edu

Educational Background

  • Ph.D. (2018) Stanford University

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

Fall 2021

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.