About me

I am a C.L.E. Moore Instructor at MIT. Previously, I completed my Ph.D. in Mathematics at ETH Zürich and I graduated in 2018 from University of Pisa and Scuola Normale Superiore.

I am currently on leave from MIT to spend the Fall semester 2024 in SLMath as a Huneke postdoctoral fellow.

My research field is Geometric Analysis. More specifically, I focus on the study of minimal surfaces.

Contact

Department of Mathematics
Massachusetts Institute of Technology
77 Massachusetts Ave
Cambridge, MA 02139

Email: gfranz@mit.edu

Research

Preprints

Genus one critical catenoid (with D. Ketover and M. Schulz), preprint.
Topological control for min-max free boundary minimal surfaces (with M. Schulz), preprint.

Publications

Estimating the Morse index of free boundary minimal hypersurfaces through covering arguments (with S. Cordero-Misteli), J. Reine Angew. Math. 807 (2024), 187-220. (arXiv:2206.02105)
On the stability of minimal submanifolds in conformal spheres (with F. Trinca), J. Geom. Anal. 33 (2023), no. 10, 335. (arXiv:2211.01106)
Equivariant index bound for min-max free boundary minimal surfaces, Calc. Var. Partial Differential Equations 62 (2023), no. 7, Paper No. 201. (arXiv:2110.01020)
Free boundary minimal surfaces with connected boundary and arbitrary genus (with A. Carlotto and M. Schulz), Camb. J. Math. 10 (2022), no. 4, pp. 835-857. See gallery here. (arXiv:2001.04920)
Inequivalent complexity criteria for free boundary minimal surfaces (with A. Carlotto), Adv. Math. 373 (2020), 107322, 68 pp. (arXiv:1908.04709)

Thesis

Contributions to the theory of free boundary minimal surfaces, Ph.D. thesis, ETH Zurich (May 2022), Advisor: Alessandro Carlotto. (arXiv:2208.12188)
Construction of alpha-harmonic maps between spheres, Master thesis, University of Pisa (July 2018), Advisor: Andrea Malchiodi.

Teaching

MIT

Spring 2024: Real Analysis 18.100B
Fall 2023: Differential Geometry 18.950
Spring 2023: Real Analysis 18.100B
Autumn 2022: Teaching assistant for Calculus 18.02

ETH Zürich

Spring 2022: Coordinator of the Seminar on Minimal Surfaces
Spring 2021: Organizer for Mass und Integral
Autumn 2020: Organizer for Functional Analysis I
Spring 2020: Organizer for Topology
Autumn 2019: Coordinator of the Seminar on Minimal Surfaces
Spring 2019: Teaching assistant for Differential Geometry II
Autumn 2018: Coordinator of the Seminar Introduction to Optimal Transport