E-mail:

beach (at) mpim-bonn (dot) mpg (dot) de

About Me:

I am currently a postdoc at MPIM Bonn. I graduted from the mathematics PhD program at the University of Toronto in 2026. My main research field is Riemannian geometry. In my spare time, I enjoy birdwatching and making art.

Papers:

(in order of preprint completion)

• I. Beach. The Shortest Geodesic Flower on a Manifold with Locally Convex Ends and Finite Volume. 2026. arXiv:2605.12642.
• I. Beach, H. Contreras Peruyero, E. Griffin, R. Rotman, C. Searle. Lengths of Orthogonal Geodesic Chords on Riemannian Manifolds. 2025. arXiv:2509.19620.
• I. Beach. Short Simple Orthogonal Geodesic Chords on a 2-Disk with Convex Boundary. Journal of Topology and Analysis. 2026. Accepted. 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. Transactions of the American Mathematical Society. 2026. Vol. 379 (9), p. 6267-6296. arXiv:2407.12673. DOI:10.1090/tran/9672.
• 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.

Presentations:

• 2026. The Quantitative Geometry of Geodesic Nets. AMS Spring Eastern Sectional Meeting. Boston, MA, United States.
• 2025. The Quantitative Geometry of Geodesics. Northwestern University Analysis Seminar. Evanston, IL, United States.
• 2025. Quantitative Topology and Geodesics. Yau Mathematical Sciences Centre Geometry Seminar. Online.
• 2025. Quantitative Topology and Geodesics. Pennsylvania State University Geometry Lunch Seminar. State College, PA, United States.
• 2025. The Quantitative Geometry of Geodesics. Centro de Ciencias Matematicas UNAM Geometry and Dynamics Seminar. Online.
• 2025. The Quantitative Geometry of Geodesics. HIM Metric Analysis Trimester Program Seminar. Bonn, NRW, Germany.
• 2025. Short Simple Orthogonal Geodesic Chords. AMS Joint Mathematics Meetings. Seattle, WA, United States.
• 2024. The Quantitative Geometry of Geodesics. SLMath Graduate Student Seminar. Berkeley, CA, United States.
• 2024. Short Simple Geodesic Loops on a 2-sphere. AMS Joint Mathematics Meetings. San Francisco, CA, United States.
• 2023. The Length of the Shortest Closed Geodesic on a Surface of Finite Area. AMS Joint Mathematics Meetings. Boston, MA, United States.
• 2023. The Length of the Shortest Closed Geodesic on a Surface of Finite Area. University of Oregon Topology/Geometry Zoom Seminar. Online.
• 2022. The Length of the Shortest Closed Geodesic on a Surface of Finite Area. Midwest Geometry Conference. Wichita, KS, United States.
• 2021. The Length of the Shortest Closed Geodesic on a Surface of Finite Area. AMS Spring Eastern Sectional Meeting. Online.
• 2019. The Beauty of the Hyperbolic Plane. CUMC. Online.

Teaching:

University of Toronto:

• Spring 2025: MAT187 (Calculus II) (Instructor)
• Spring 2024: MAT224 (Linear Algebra II) (TA)
• Fall 2023: MAT464/MAT1342 (Riemannian Geometry) (TA)
• Summer 2023: MAT135 (Calculus I) (TA)
• Spring 2023: MAT247 (Algebra II) (TA)
• Fall 2022: MAT240 (TA), MAT464/MAT1342 (Riemannian Geometry) (TA)
• Spring 2022: MAT224 (Linear Algebra II) (Grading TA)
• Fall 2021: MAT464/MAT1342 (Riemannian Geometry) (TA)
• Summer 2021: MAT133 (Calculus and Linear Algebra for Commerce) (Lecture TA)
• Spring 2020: MAT136 (Calculus II) (TA)
• Fall 2019: MAT135 (Calculus I) (TA)

Workshops/Fellowships:

• Banff International Research Station Oaxaca, Mixtures of Probability and Geometry, May 25 - May 30 2025
• Hausdorff Research Institute of Mathematics, Metric Analysis Trimester Program, Feb 16 - Feb 23 2025.
• SLMath, Program Associate SLMath Doctoral 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 Graduate School, July 11 - July 22 2022

Other Activities:

• I helped design the newsletter for the University of Toronto Mathematics Graduate Student Association.
• I designed the poster for the 2023, 2024, and 2025 Bird's Eye Conference at the University of Toronto.