📌 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

📌 Upcoming talks

• “Multiplicity of Solutions for Gross-Pitaevskii equations on Riemannian Manifolds”, 25-29 May 2026
  International Conference on Elliptic and Parabolic Problems: GAETA-2026
  🔗 Previus Talks

📌 Research 

My work focuses on Geometric Analysis, Variational Methods, and Dynamical Systems.
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Selection of Recent Papers
(Below is a short selection of recent publications and preprints. [🔗 Full list here])

• D. Corona, S. Nardulli, R. Oliver-Bonafoux, G. Orlandi,
  “Multiplicity of solutions for Gross-Pitaevskii equations on Riemannian manifolds”,
  Preprint, 2025 🔗 arXiv:2511.21349

• J.H. Andrade, D. Corona, S. Nardulli, P. Piccione, R. Ponciano,
  “From bubbles to clusters: Multiple solutions to the Allen-Cahn system”,
  Journal of Differential Equations, 2026
  🔗 doi: 10.1016/j.jde.2026.114189

• 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

📌 Teaching 

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