Since September 2026, I am a Dickson Instructor at the University of Chicago. My mentor is André Neves.
I was a PhD student at ETH Zürich under the supervision of Tristan Rivière.
I am interested in Geometric Analysis.
You can contact me at mgianocca@uchicago.edu.
Papers
6. (with O. Chodosh) Minimal hypersurfaces of Morse index one, preprint (2026).
5. Note on energy index of minimal surfaces in spheres, preprint (2025).
4. Rigidity in the Ginzburg-Landau approximation of harmonic spheres, preprint (2025).
3. (with F. Da Lio) Morse Index Stability for the Ginzburg-Landau Approximation, preprint (2024).
2. Optimal weighted Wente’s inequality, Comm. PDE
1. (with F. Da Lio and T. Rivière) Morse Index Stability for Critical Points to Conformally invariant Lagrangians, JEMS
Mediations
1. (with O. Chodosh) No compromise in the liquid drop model (2026)
The conversation ran to about eighty prompts. Most asked for clarification, verification, rewriting, or further development, and some were prompted by ideas arising in our ongoing discussions. A few suggested natural geometric directions, including outward minimality, stability, symmetrization, and ideas from Agostiniani and Mazzieri, but none contained the key estimate. I have not made the exchange public because it was private, often casual to the point of embarrassment, and says little by itself about the interaction between mathematicians and LLMs. Our contribution was the mathematical work that followed. We identified what the proof really needed, simplified and checked the argument, reduced its reliance on outside results where possible, placed it correctly in the literature, and wrote it in a form that a human reader could readily follow. The GPT output obtained after several requests for substantial improvement, but before any rewriting by us, is available here.
Teaching
Spring 26: none