Lorenzo Sarnataro

Department of Mathematics
University of Toronto
40 St George St
Toronto, Ontario M5S 2E4
Canada

email: lorenzo.sarnataro [at] utoronto.ca

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I am a Brauer Postdoctoral Fellow at the University of Toronto. My mentors are Robert Haslhofer and Yevgeny Liokumovich.

I received my PhD at Princeton University in 2024, where I was advised by Fernando Codá Marques.

Here is my CV.

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Research interests: Geometric Analysis, Minimal Surfaces, Geometric Flows.

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Research

1. Allen-Cahn construction of free boundary minimal hypersurfaces
   (Joint with Martin Li and Davide Parise) in preparation

2. Existence of free boundary minimal disks in convex regions
   (Joint with Douglas Stryker, Zhichao Wang, and Xin Zhou) arXiv:2606.02396

3. Index, intersections, and multiplicity of min-max geodesics
   (Joint with Jared Marx-Kuo and Douglas Stryker) arXiv:2410.02580

4. Boundary behavior of limit-interfaces for the Allen-Cahn equation on Riemannian manifolds with Neumann boundary condition
   (Joint with Martin Li and Davide Parise) arXiv:2312.07210 — Arch. Ration. Mech. Anal. 248 (2024)

5. Existence of closed embedded curves of constant curvature via min-max
   (Joint with Douglas Stryker) arXiv:2306.04840 — Reine Angew. Math. (Crelle’s Journal), vol. 2026, no. 831

6. Optimal regularity for minimizers of the prescribed mean curvature functional over isotopies
   (Joint with Douglas Stryker) arXiv:2304.02722 — Cambridge Journal of Mathematics, Vol. 13 (2025), no. 3

Talks

Teaching

At the University of Toronto:

At Princeton University: