Assistant Professor

Department of Mathematics and Statistics

Binghamton University

Email: sapir@math.binghamton.edu

Slides from a talk on A projection from filling currents to Teichmuller space .

A talk on Tesselations from long geodesics on surfaces at the conference on the Mathematical Legacy of Maryam Mirzakhani at Stanford in 2018, recorded by Zala films.

Slides from a talk on Applications of a combinatorial model for curves on surfaces from 2016. This includes counting results and the construction of metrics where curves are short.

A poster about Non-simple geodesics on surfaces I made in Inkscape for an ICERM workshop on Low-dimensional Topology, Geometry, and Dynamics in 2013. If you're curious about the underlying svg file, it's here.

A talk on Counting non-simple closed curves on surfaces given at the Geometry, Groups and Dynamics/GEAR Seminar in 2014. (If you want to amuse yourself, turn on the automatically generated subtitles.)

- Sapir, J. An extension of the Thurston metric to projective filling currents. Geom Dedicata.
**218**(2024), 78, 1-18. Arxiv version - Dozier, B., Sapir, J. Simple vs non-simple loops on random regular graphs. J. Graph Theory.
**105**(2024), 4, 562–579. Arxiv version - Dozier, B., Sapir, J. Counting geodesics on expander surfaces. arXiv:2304.07938.
- Hensel, S., Sapir, J. A projection from filling currents to Teichmuller space. Proc. Amer. Math. Soc.
**151**(2023), 8, 3621-3633. Arxiv version - Sapir, J. A length comparison theorem for geodesic currents. arXiv:2210.00925.
- Dozier, B., Sapir, J. Coarse density of subsets of moduli space. Ann. Inst. Fourier (Grenoble)
**71**(2021), 3, 1121-1134. Arxiv version - Athreya, J., Lalley, S., Sapir, J., Wroten, M. Local geometry of random geodesics on negatively curved surfaces. Ann. H. Lebesgue
**4**(2021), 187-226. Arxiv version - Sapir, J. A Birman-series type result for geodesics with infinitely many self-intersections. Transactions of the American Mathematical Society,
**374**(2021), 11, 7553--7568. Arxiv version - Aougab, T., Gaster, J., Patel, P., & Sapir, J. Building hyperbolic metrics suited to closed curves and applications to lifting simply. Mathematical Research Letters,
**24**(2017), 3, 593–617. Arxiv version - Sapir, J. Orbits of non-simple closed curves on a surface. arXiv:1602.09093
- Sapir, J. Bounds on the number of non-simple closed geodesics on a surface. International Mathematics Research Notices,
**2016**(2016), 24, 7499-7545. Arxiv version - Sapir, J. Lower bound on the number of non-simple closed geodesics on surfaces.Geom Dedicata,
**184**(2016), 1-25. Arxiv version - Bleak, C., Bowman, H.E., Lynch, A.G., Graham, G., Hughes, J., Matucci, F., & Sapir, E. Centralizers in the R. Thompson group Vn.Groups, Geometry, and Dynamics,
**7**(2013), 821-865. Arxiv version - Chestnut, J., Sapir, J., & Swartz, E. Enumerative properties of triangulations of spherical bundles over $S^1$. Eur. J. Comb.,
**29**(2008), 662-671. Arxiv version