📌 Short Presentation 

I am a researcher in Mathematical Analysis, working on Geometric Analysis, Variational Methods, and Hamiltonian Systems.
My research focuses on the interplay between geometry and analysis, with applications in differential equations and dynamical systems.
I am also dedicated to teaching and mentoring students at various levels, from undergraduate to PhD courses.

🔗 Short CV 🔗 Updated CV

📌 Research 

My work focuses on Geometric Analysis, Variational Methods, and Dynamical Systems.
[🔗 Learn more]

Selection of Recent Papers
(Below is a short selection of recent publications and preprints. [🔗 Full list here])

• J.H. Andrade, D. Corona, S. Nardulli, P. Piccione, R. Ponciano
  “From bubbles to clusters: Multiple solutions to the Allen--Cahn system”,
  Preprint, 2024 🔗 arXiv:2410.17026

• D. Corona, S. Nardulli, R. Oliver-Bonafoux, G. Orlandi, P. Piccione
  “Multiplicity results for mass constrained Allen-Cahn equations on Riemannian manifolds with boundary”
  Mathematische Annalen, 2025
  🔗 doi: 10.1007/s00208-025-03178-7

• D. Corona, R. Giambò, P. Piccione,
  “A note on the regularity and the existence of Riemannian splines”,
  Mathematics of Control, Signals, and Systems, 2025
  🔗 doi: 10.1007/s00498-025-00414-y

• E. Caponio, D. Corona, R. Giambò, P. Piccione,
  “Fixed energy solutions to the Euler-Lagrange equations of an indefinite Lagrangian with affine Noether charge”,
  Annali di Matematica Pura e Applicata, 2024
  🔗 doi: 10.1007/s10231-024-01424-4

📌 Upcoming talks

• “Multiplicity results for the Allen-Cahn equation in compact Riemannian manifolds”, July 2025
  MCA 2025 (Mathematical Congress of the Americas), Miami, USA

🔗 Previus Talks

📌 Teaching 

I teach courses at both undergraduate and graduate levels, including PhD courses.
🔗 Learn more