Ian M Adelstein

Yale University


I work in geometric analysis and global differential geometry, using variational methods to study closed geodesics.

I organized a workshop on Geometric and Topological Methods in Data Science at ICERM on December 16-17, 2021.

Here are some papers:

  1. Besse projective spaces with many diameters. (with F. Vargas Pallete).

  2. The length of the shortest closed geodesic on positively curved 2-spheres. (with F. Vargas Pallete) to appear in Math Z.

  3. Characterizing round spheres using half-geodesics. (with B. Schmidt) Proc. Nat. Acad. Sci., 116 (2019), 14501-14504.

  4. Minimizing geodesic nets and critical points of distance. Diff. Geo. and its Applications, 70 (2020), 101624.

  5. Existence and non-existence of half-geodesics on the 2-sphere. Proc. Amer. Math Soc., 144 (2016), 3085-3091.

  6. Minimizing closed geodesics via critical points of the uniform energy. Math. Res. Lett., 23 (2016), 953-972.

  7. The G-invariant spectrum and non-orbifold singularities. (with M. Sandoval) Archiv der Math., 109 (2017), 563-573.

Here is my arxiv page. Here is my CV.

I gave an invited talk at the 2020 Virtual Workshop on Ricci and Scalar Curvature.

I co-organized a workshop on Filling Volumes, Geodesics, and Intrinsic Flat Convergence with Christina Sormani at Yale.

Undergraduate Research

The study of closed geodesics is super accessible to undergraduate students, especially when considered on flat surfaces or as billiard paths on polygons. I have led a number of undergraduate research projects, and am the director of the SUMRY program at Yale. Here are a few papers appropriate for an undergraduate student:

  1. Reframing the Pythagorean theorem (slides)

  2. Closed geodesics on doubled polygons (read this one first)

  3. Minimizing closed geodesics on polygons and disks (read this one second)

  4. Oblivious points on translation surfaces

  5. Geodesic nets on flat spheres

  6. Reflections from SUMRY: Learning to communicate mathematics verbally


I am a passionate educator and create an engaging and inclusive classroom when I teach. I employ active pedagogy and have a dynamic teaching style that is adaptable to diverse students, classrooms, and material. I've enjoyed teaching across the undergraduate mathematics curriculum, and have a strong belief that when math is taught in an engaging and inclusive environment every student is capable of learning and success.

If you are a student, please stop by my office DL 419 anytime; if you are an educator, I am always excited to chat about teaching.