معرفی
Luigi Appolloni is a Research Fellow in Geometric Analysis within the School of Mathematics at the University of Leeds, mentored by Dr Ben Sharp. He joined the university in May 2023 and is actively engaged in research at the intersection of partial differential equations and differential geometry.
Dr. Appolloni completed his academic journey with a Bachelor's Degree in Mathematics from the University of Perugia in 2015, followed by a Master's Degree from the same institution in 2018 under the supervision of Professors D. Mugnai and P. Pucci. He earned his PhD in Mathematics from the University of Milan-Bicocca in 2023, supervised by Professor Simone Secchi.
Dr. Appolloni's research focuses on the intersection of partial differential equations and differential geometry. During his PhD, he studied existence of solutions to semilinear and quasilinear PDEs using variational and topological methods, particularly addressing problems with loss of compactness. His recent work has shifted toward PDEs arising from differential geometry, with emphasis on minimal/CMC surfaces and harmonic maps. He is particularly investigating the bubbling phenomenon along sequences of solutions, which represents a critical area in geometric analysis.
Dr. Appolloni has established himself as a productive researcher with multiple publications spanning from 2021 to 2025. His work demonstrates a clear progression from foundational PDE theory to more specialized geometric applications. His publications reveal a consistent focus on critical problems, nonlocal operators, and variational methods, with recent work showing increased specialization in geometric contexts including Cartan-Hadamard manifolds and harmonic maps.
Dr. Appolloni is actively engaged in the academic community through teaching and professional activities. He has taught courses including Differentiable Manifolds through the MAGIC Consortium and provided tutorials for Sequences and Series at the University of Leeds. He has presented his research at numerous seminars and conferences across Europe and has undertaken research visits to institutions including the University of Western Australia, Scuola Normale Superiore in Pisa, and Universidad de Granada.
Additionally, Dr. Appolloni has organized academic events including the Bilux Ph.D. Meeting at the University of Milan-Bicocca and the 'Insalate di Matematica' seminar series, demonstrating leadership in fostering academic collaboration among early-career researchers.
