Introduction:

My name is Juliet Aygun, and I am a fourth year math graduate student and Simons Dissertation Fellow at Cornell University. My advisor is Ben Dozier. I was an undergraduate student at Purdue University during 2018-2022, advised under Jeremy Miller and Manuel Rivera. I am originally from the Chicago area.

My research concerns flat surfaces (e.g. k-differentials, translation surfaces), but more generally I study hyperbolic geometry, Teichmüller theory, and low-dimensional topology.

Here is my CV.

Email: ja742 [at] cornell [dot] edu

Research:

  1. Counting geodesics on prime-order k-differentials, arXiv:2506.24084, submitted.
  2. Realizing pairs of multicurves as cylinders on translation surfaces with J. Barkdoll, A. Calderon, J. Lorman, T. Sandstrom, Algebraic & Geometric Topology (2025), arXiv:2404.08096.
  3. A degree theorem for the simplicial closure of Auter space with J. Miller, Homology, Homotopy, and Applications (2024), arXiv:2208.12358v2.

Upcoming Travel:

  • Binghamton Geometry and Topology seminar, January 2026
  • UW-Madison Group Actions and Dynamics seminar, March 2026
  • SLMath, March 2026
  • AMS Sectional Meeting at Boston College, March 2026
  • Cornell Topology Festival, May 2026
  • IAS, June 2026

Selected Talks:

  • Counting cylinders on (1/k)-translation surfaces, BUGCAT – Binghamton, November 2025
  • Counting geodesics on prime-order k-differentials, Rice Analysis Seminar, October 2025
  • Counting geodesics on prime-order k-differentials, CUNY Complex Analysis and Dynamics Seminar, September 2025
  • Realizing pairs of multicurves as cylinders on translation surfaces, Graduate Student Conference in Algebra, Geometry, and Topology – Temple, May 2024
  • General flat structures on Riemann surfaces, BUGCAT – Binghamton, November 2023
  • Realizing pairs of multicurves as cylinders on translation surfaces, University of Buffalo Graduate Student Seminar, March 2023
  • Cylinder Configurations on Flat Surfaces, MAA Mathfest Undergraduate Student Paper Session, August 2021
  • The Riemannian Geometry of Almost Abelian Groups, Young Mathematician Conference – Ohio State University (Virtual), August 2020

Conferences:

  • Binghamton University Graduate Combinatorics, Algebra, and Topology Conference (BUGCAT), Binghamton, NY, November 2025
  • Mathematical Congress of the Americas (MCA 2025), Miami, Florida, July 2025
  • Dynamics and Rigidity: a Celebration of the Mathematics of Alex Eskin, Cetraro, Italy, July 2025.
  • Hyperbolic Manifolds, Their Submanifolds and Fundamental Groups, Rio de Janeiro, Brazil, January 2025.
  • Binghamton University Graduate Combinatorics, Algebra, and Topology Conference (BUGCAT), Binghamton, NY, October 2024
  • Canaryfest – Moving to higher rank: from hyperbolic to Anosov, Cetraro, Italy, July 2024
  • Graduate Student Conference in Algebra, Geometry, and Topology, Philadelphia, PA, May 2024
  • Cornell Topology Festival, Ithaca, NY, May 2024
  • 8th Iberoamerican Congress on Geometry, Pucón, Chile, December 2023
  • Binghamton University Graduate Combinatorics, Algebra, and Topology Conference (BUGCAT), Binghamton, NY, November 2023
  • ISM Discovery School: Geometry and spectra of random hyperbolic surfaces, Montréal, Canada, June 2023
  • Groups and Dynamics in Geometry, Ascona, Switzerland, May 2023
  • Cornell Topology Festival, Ithaca, NY, May 2023
  • Binghamton University Graduate Combinatorics, Algebra, and Topology Conference (BUGCAT), Binghamton, NY, November 2022

Awards:

  • Eleanor Norton York Award
  • Simons Dissertation Fellow
  • Purdue Outstanding Senior in the College of Science
  • Purdue Senior Achievement Award in Mathematics
  • Eugene V. Schenkman Award
  • Leonard D. & Anna W. Berkovitz Scholar

Teaching:

  • Fall 2025 – Spring 2026: TA for MATH 1106: Modeling with Calculus for the Life Sciences
  • Fall 2023 – Fall 2024: TA for MATH 1910: Calculus for Engineers

Links: