E-mail:

isabel (dot) beach (at) mail (dot) utoronto (dot) ca

About Me:

I am a mathematics PhD student at the University of Toronto. My main research interest is quantitative geometry.

Papers:

• I. Beach. Short Simple Orthogonal Geodesic Chords on a 2-Disk with Convex Boundary. arXiv:2507.07797.
• I. Beach, H. Contreras Peruyero, R. Rotman, and C. Searle. Linear Bounds for the Lengths of Geodesics on Manifolds With Curvature Bounded Below. Journal of Geometric Analysis. 2025. Vol. 35, article number 217. arXiv:2410.10975. DOI:10.1007/s12220-025-02003-6.
• I. Beach. Short Simple Geodesic Loops on a 2-Sphere. 2024. arXiv:2407.12673
• I. Beach and R. Rotman. The Length of the Shortest Closed Geodesic on a Surface of Finite Area. Proceedings of the American Mathematical Society. 2020. Vol. 148 (12), p. 5355-5367. arXiv:1912.07711. DOI:10.1090/proc/15194.

In Preparation:

• I. Beach, H. Contreras Peruyero, E. Griffin, R. Rotman, C. Searle. Lengths of Orthogonal Geodesic Chords on Riemannian Manifolds.

Presentations:

• HIM Metric Geometry Spring 2025 Trimester Program Seminar. The Quantitative Geometry of Geodesics.
• JMM 2025. The Quantitative Geometry of Geodesics.
• SLMath Graduate Student Seminar Fall 2024. The Quantitative Geometry of Geodesics.
• JMM 2024. Short Simple Geodesic Loops on a 2-Sphere. PDF slides.
• JMM 2023. The Length of the Shortest Closed Geodesic on a Surface of Finite Area. PDF slides.
• Topology/Geometry Zoom Seminar 2022. The Length of the Shortest Closed Geodesic on a Surface of Finite Area. (With additional discussion on the Seifert conjecture). PDF slides.
• Midwest Geometry Conference 2022. The Length of the Shortest Closed Geodesic on a Surface of Finite Area.
• AMS Spring Eastern Meeting 2021. The Length of the Shortest Closed Geodesic on a Surface of Finite Area. PDF slides.
• CUMC 2019. The Beauty of the Hyperbolic Plane. Powerpoint slides.

Teaching:

• Spring 2025: MAT187 (Instructor)
• Spring 2024: MAT224 (TA)
• Fall 2023: MAT464/MAT1342 (TA)
• Summer 2023: MAT135 (TA)
• Spring 2023: MAT247 (TA)
• Fall 2022: MAT240 (TA), MAT464/MAT1342 (TA)
• Spring 2022: MAT224 (Grading TA)
• Fall 2021: MAT464/MAT1342 (TA)
• Summer 2021: MAT133 (Lecture TA)
• Spring 2020: MAT136 (TA)
• Fall 2019: MAT135 (TA)

Workshops:

• Banff International Research Station Oaxaca, Mixtures of Probability and Geometry, May 25 - May 30 2025
• SLMath, Program Associate Fellowship (New Frontiers in Curvature), August 19 - December 20 2024
• Institute for Advanced Study, Summer Collaborators Program, July 3 - July 31 2024
• Banff International Research Station, Women in Geometry 3, September 24 - September 29 2023
• MSRI/University of Oxford, Metric Geometry and Geometric Analysis Summer Gradute School July 11 - July 22 2022

Design:

• I helped design the newsletter for the University of Toronto Mathematics Graduate Student Association.
• I designed the poster for the 2023 and 2024 Bird's Eye Conference.