Francisco Torres de Lizaur
Department of Mathematical Analysis
Faculty of Mathematics, University of Seville
My research interests include the analysis of PDEs, geometry and dynamical systems.
I am currently a Ramón y Cajal (tenure-track) researcher at the Faculty of Mathematics of the University of Seville. Before that, I was a postdoctoral fellow at the University of Toronto and at the Max-Planck Institute for Mathematics in Bonn.
Research
(with R. Cardona) Contact type solutions and non-mixing of the 3D Euler equations, Arxiv
(with A. Enciso and D. Peralta-Salas) Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher. J. Differential Equations 354 (2023), 170–182 , Arxiv
(with A. D Martínez) Sign equidistribution of Legendre polynomials, Anal. Math. Phys. (2023), Arxiv
(with A. Enciso and D. Peralta-Salas) Limiting measures and energy growth for sequences of solutions to Taubes's Seiberg-Witten equations, J Geom Anal 33, 269 (2023), Arxiv
Chaos in the incompressible Euler equation on manifolds of high dimension, Invent. Math. (2022), Arxiv
(with A. D Martínez) Distribution symmetry of toral eigenfunctions, Rev. Mat. Iberoamericana (2021).
Periodic orbits of analytic Euler fields on 3-manifolds, Arxiv
Geometric structures in the nodal sets of eigenfunctions of the Dirac operator, Arxiv
(with D. Peralta-Salas and A. Rechtman) A characterization of 3D steady Euler flows using commuting zero-flux homologies, Ergodic Theory Dynam. Systems 41 (2021), no. 7, 2166–2181, Arxiv
(with A. Enciso and D. Peralta-Salas) High-energy eigenfunctions of the Laplacian on the torus and the sphere with nodal sets of complicated topology, in S. Koike ( Ed. ), Nonlinear Partial Differential Equations for Future Applications, Singapore: Springer, Arxiv
(with A. Enciso and D. Peralta-Salas) Helicity is the only integral invariant of volume-preserving transformations. Proc. Natl. Acad. Sci. USA 113 (2016), no. 8, 2035–2040, Arxiv
(with A. Enciso and D. Peralta-Salas) Knotted structures in high-energy Beltrami fields on the torus and the sphere. Ann. Sci. Éc. Norm. Supér. (4) 50 (2017), no. 4, 995–1016, Arxiv
Here you can find my PhD dissertation, which I defended on June 14, 2018 at Universidad Autónoma de Madrid.