Francesco Cattafi

Francesco Cattafi is a post-doctoral researcher in differential geometry at the Chair of Mathematics X (Geometry) of Julius-Maximilians-Universität Würzburg, funded by the DFG Walter Benjamin Programme. He conducts research on Lie groupoids/algebroids, Cartan geometries and the geometry of PDEs, and is currently on the academic job market for positions starting Fall 2025.

Education

• PhD in Mathematics (2015–2020) – Universiteit Utrecht, The Netherlands
• MSc in Mathematics (2013–2015) – Università degli Studi di Torino, Italy
• BSc in Mathematics (2010–2013) – Università degli Studi di Torino, Italy

Research Interests

Cattafi's work lies at the intersection of differential geometry, Lie theory and the geometric theory of PDEs. His primary focus is on Lie groupoids and algebroids, investigating their role in describing symmetries and equivalences of geometric structures. He studies Cartan geometries and G-structures to understand integrability via multiplicative forms and Pfaffian systems. A recurring theme is translating analytic questions about PDEs into geometric problems involving Lie pseudogroups and Morita equivalences.

Publications Overview

Since 2016 Cattafi has authored or co-authored seven peer-reviewed papers spanning foundational aspects of transitive differential geometry and applications to Poisson and symplectic geometry. Early work with Palese and Winterroth explored variational calculus and Noether currents, while his PhD-era collaborations with Crainic and Salazar linked PDE analysis to Pfaffian fibrations. Recent preprints treat PB-groupoids versus VB-groupoids and novel groupoid-theoretic approaches to symmetry and equivalence problems.

Grants & Fellowships

• DFG Walter Benjamin Fellowship (2021–present) – Julius-Maximilians-Universität Würzburg
• Junior Research Fellowship (2021) – Erwin Schrödinger Institute, Vienna
• Post-doctoral grant (2021) – Wolfgang Pauli Institute, Vienna
• Post-doctoral grant (2020) – KU Leuven, Belgium

Contact & Online Presence

Room 00.003, Building 31 (Physics East), Emil-Fischer-Straße 31, 97074 Würzburg, Germany
Email: francesco.cattafi@uni-wuerzburg.de
ORCID: 0000-0001-9785-0770