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Dr Luigi Appolloni

Foto di Luigi Appolloni

Welcome to my personal webpage. I am Luigi Appolloni, a Research Fellow in Geometric Analysis within the School of Mathematics at the University of Leeds, mentored by Dr Ben Sharp.

Previously, I completed a Ph.D. in Mathematics at the Università degli Studi di Milano-Bicocca under the supervision of Professor Simone Secchi. Here you can find details about my research interests, publications, and academic activities.

Please feel free to reach out if you have any questions or would like to connect!

Email: l.appolloni[at]leeds.ac.uk

Address:
School of Mathematics
University of Leeds
Leeds, LS2 9JT
UK

ORCID: 0000-0003-2437-7083

Scientific Interests

During my Ph.D., I studied the existence of solutions to some semilinear and quasilinear PDEs, involving both local and non-local operators. I used variational and topological methods to study problems where there was a loss of compactness, either due to the unboundedness of the domain or the presence of a critical Sobolev exponent.

More recently, I have become interested in PDEs arising from differential geometry, in particular minimal/CMC surfaces and harmonic maps. In this context, I am working on better understanding the so-called bubbling phenomenon along a sequence of solutions.

Employment

  • May 2023 – Present: Research Fellow in Geometric Analysis, University of Leeds. Supervisor: Dr B. Sharp.

Education

  • 2023 - PhD in Mathematics, Università degli Studi di Milano-Bicocca. Supervisor: Professor S. Secchi.
  • 2018 - Master’s Degree in Mathematics, Università degli Studi di Perugia. Supervisor: Professor D. Mugnai and Professor P Pucci.
  • 2015 - Bachelor’s Degree in Mathematics, Università degli Studi di Perugia.

Teaching

  • 2024 / 2025: MAGIC Course on Differentiable Manifolds, MAGIC Consortium.
  • 2023 / 2024: Tutorial Sets for Sequences and Series (MATH1026), University of Leeds.
  • 2023 / 2024: Minicourse on Fractional Sobolev Spaces and Variational Methods for Critical Kirchhoff Problems, University of Leeds.
  • 2021 / 2022: Preparatory Course in Mathematics, Università degli Studi di Milano-Bicocca.
  • 2021 / 2022: Teaching Assistant for Calculus I, Università degli Studi di Bergamo.
  • 2020 / 2021: Preparatory Course in Mathematics, Università degli Studi di Milano-Bicocca.

Publications

Published papers

  • L. Appolloni, A non-local p-Kirchhoff critical problem without the Ambrosetti-Rabinowitz condition, J. Math. Anal. Appl., 2025.Link
  • L. Appolloni, G. Molica Bisci, S. Secchi, A note on the nonlinear Schrödinger equation on Cartan-Hadamard manifolds with unbounded and vanishing potentials, Math. Methods Appl. Sci., 2024.Link
  • L. Appolloni, G. M. Bisci, S. Secchi, Multiple solutions for Schrödinger equations on Riemannian manifolds via ∇-theorems, Annals of Global Analysis and Geometry, 2023.Link
  • L. Appolloni, G. Molica Bisci, S. Secchi, Schrödinger equation on Cartan-Hadamard manifolds with oscillating nonlinearities, J. Math. Anal. Appl., 2023.Link
  • L. Appolloni, A. Fiscella, S. Secchi, A perturbed fractional p-Kirchhoff problem with critical nonlinearity, Asymptotic Analysis, 2022.Link
  • L. Appolloni, G. Molica Bisci, S. Secchi, On critical Kirchhoff problems driven by the fractional Laplacian, Calc. Var. Partial Differential Equations, 2021.Link
  • L. Appolloni, D. Mugnai, Fractional weighted problems with a general nonlinearity or with concave-convex nonlinearities, Math. Methods Appl. Sci., 2021.Link
  • L. Appolloni, S. Secchi, Normalized solutions for the fractional NLS with mass supercritical nonlinearity, J. Differential Equations, 2021.Link

Preprints

  • L. Appolloni, R. Molle, Normalized Schrödinger equations with mass-supercritical nonlinearity in exterior domains, arXiv:2503.09262.
  • L. Appolloni, B. Sharp, A note on moving frames along Sobolev maps and the regularity of weakly harmonic maps, arXiv:2502.18078.

Seminars

  • January 2025 – University of Warsaw, Workshop for young researchers in PDEs.
  • September 2024 – Università degli Studi di Milano-Bicocca and Università degli Studi di Milano Statale, Young Researchers Meeting on PDEs.
  • September 2024 – Scuola Normale Superiore, Pisa (Internal seminar).
  • July 2024 – European Congress of Mathematics 2024, Seville.
  • May 2024 – International Conference on Elliptic and Parabolic Problems, Gaeta.
  • April 2024 – Università degli Studi di Roma "Tor Vergata" (Internal seminar).
  • July 2022 – Università degli Studi di Urbino, Two Nonlinear Days in Urbino 2022.
  • December 2022 – Università degli Studi di Milano-Bicocca (Internal seminar, "Insalate di Matematica").
  • October 2022 – Università degli Studi di Milano-Bicocca, Bilux Ph.D. Meeting.
  • May 2022 – Universidad de Granada (Internal seminar).

Research Visits

  • November/December 2024: University of Western Australia. Invited by: Professor S. Dipierro and Professor E. Valdinoci.
  • September 2024: Scuola Normale Superiore, Pisa. Invited by: Professor A. Malchiodi.
  • April 2024: Università degli Studi di Roma "Tor Vergata". Invited by: Professor R. Molle.
  • April/May 2022: Universidad de Granada. Invited by: Professor D. Ruiz.
  • July 2022: Università degli Studi di Urbino Carlo Bo. Invited by: Professor G. Molica Bisci.

Organised Conferences

  • October 2024: Bilux Ph.D. Meeting, Università degli Studi di Milano-Bicocca.
  • 2020 - 2022: Insalate di Matematica , Series of seminars at the Università degli Studi di Milano-Bicocca.