Roberto Svaldi

Current Position:
Associate Professor at the Department of Mathematics of Università degli Studi di Milano.

Previous Positions:
I obtained my doctoral degree from the Department of Mathematics at Massachusetts Institute of Technology in 2015, under the supervision of James M^cKernan.
From September 2022 until December 2025 I was a Ricercatore a tempo determinato di tipo B (RTDB, tenure track researcher) at Università degli Studi di Milano. My research was funded by Program for Young Researchers 'Rita Levi Montalcini' of the Italian Ministry of Research and University.
From 2019 to 2022, I was a Bernoulli Instructor at the Institute of Mathematics of École polytechnique fédérale de Lausanne. Until the end of 2021, I was also a Marie Curie Fellow hosted by the Chair of Algebraic Geometry at EPFL working on my research project "Birational and moduli problems in algebraic geometry" (BirModProbAG).
From 2015 to 2019 I was a Research Fellow at the Department of Pure Mathematics and Mathematical Statistics of the University of Cambridge, and a Fellow and College Lecturer in Pure Mathematics at Churchill College, Cambridge.
During AY 2016/17 I held a visiting position at the Area of Mathematics of SISSA, Trieste, where I joined the group of Jacopo Stoppa as assegnista di ricerca (visiting assistant professor).

Curriculum vitae (click here for the version in Italian)

Orcid ID: 0000-0003-1489-5899.

Research Interests:
Birational geometry of higher dimensional algebraic varieties.
Geometry of Fano and Calabi-Yau varieties.
Structure of algebraic foliations with mild singularities.

Selected publications

• A geometric characterization of toric singularities,
  with J. Moraga, J. Math. Pures Appl. (9) 195 (2025), Paper No. 103620.
• A characterization of toric varieties,
  with M. Brown, J. McKernan, H. Zong, Duke Math. J., Volume 167, Number 5 (2018), 923-968.


• On moduli of foliated surfaces,
  with C. Spicer, S. Velazquez, arXiv:2511.13491.
• Local and global applications of the Minimal Model Program for co-rank one foliations on threefolds,
  with C. Spicer, J. Eur. Math. Soc. 24 (2022), no. 11, 3969-4025.


• Boundedness of some fibered K-trivial varieties,
  with P. Engel, S. Filipazzi, F. Greer, M. Mauri, arXiv:2507.00973.
• Boundedness of elliptically fibered Calabi--Yau threefolds,
  with S. Filipazzi, C. Hacon, J. Eur. Math. Soc. 27 (2025), no. 9, pp. 3583–3650.
• Boundedness of elliptic Calabi-Yau varieties with a section,
  with C. Birkar, G. Di Cerbo, J. Differential Geom. 128 (2024), no. 2, 463–519.

Full list of publications

Vacancies in Geometry/Algebra at the University of Milan (no opening currently available)

Teaching/Didattica

Cetraro lecture notes

Theses and projects: If you are a student considering undertaking a project or a thesis under my supervision, you can just get in touch with me via email to discuss my availability and what the possible options are.
Tesi di laurea e progetti di studio indipendente: gli studenti interessati ad un progetto di studio indipendente o una tesi di laurea/dottorato sotto la mia supervisione, possono contattarmi per email per discutere la mia disponibilità ed le possibili opzioni.

I support this statement of inclusiveness.

Some useful links:

Algebraic Geometry group at Università di Milano.
On writing mathematical texts (by B. Poonen).
Upcoming conference in AG (by R. Vakil)
UMI - Collaborazioni Matematiche con il Sud Globale