Phase transitions on manifolds
Multiplicity of solutions for the Allen–Cahn and Gross–Pitaevskii equations on Riemannian manifolds, with and without boundary, and their link with minimal surfaces and isoperimetric problems.
Research
31publications
26talks since 2020
5countries for invited seminars
1PhD student co-supervised
My work sits where geometry and analysis meet. I use critical point theory, Lusternik–Schnirelmann and Morse theory to find and count solutions of nonlinear equations that come from geometry and physics.
Hamiltonian systems and geodesics
Brake orbits, orthogonal geodesic chords and Euler–Lagrange orbits with boundary conditions, studied through Finsler and Riemannian geometry and variational methods for indefinite Lagrangians.
Dynamical systems
Critical exponent functions and mixing properties of interval maps, together with variational models from mechanics, such as the nonlinear Timoshenko beam.
Earlier: control theory
During my PhD I worked on optimal output regulation and tracking for redundant systems, with applications to wind turbines and to wearable devices for sign-language recognition.
Projects and grants
- MSCA Seal of Excellence (Horizon Europe, 2026), project Diffuse Interfaces in Manifolds and Metric Spaces (DIMMS).
- ICTP–INdAM Research in Pairs (2026), Trieste.
- PI, INdAM–GNAMPA project (2022–23): variational methods for Lagrangians with low regularity and indefinite Lagrangians.
- Collaborator in the FAPESP projects 2022/16097-2, 2021/05256-0 and SPRINT 23/08246-0 (Universidade de São Paulo and UFABC, Brazil).
Research stays
- São Paulo, Brazil USP 2023, 2024, 2026 (now) · UFABC 2025
- Guangdong, China Great Bay University 2025, 2026
- Cape Town, South Africa University of Cape Town 2024
- Trieste, Italy ICTP 2026
- Bratislava, Slovakia Slovak University of Technology 2018