Arnau Padrol

Arnau Padrol is an Associate Professor at the Department of Mathematics and Computer Science, Faculty of Mathematics, Universitat de Barcelona. He is a member of the Combinatorics Research Group, the Institut de Matemàtica de la Universitat de Barcelona (IMUB), and the Centre de Recerca Matemàtica (CRM). He is currently on leave from a similar position as Maitre de conférences HDR at Sorbonne Université’s Institut de Mathématiques de Jussieu - Paris Rive Gauche, where he was part of the Combinatoire et Optimisation team.

His research lies at the intersection of discrete geometry, combinatorics, and algebra, with a focus on convex polytopes, oriented matroids, triangulations, and their applications. He explores deep structural properties of polytopes, including their realization spaces, deformation cones, and connections to cluster algebras and combinatorial optimization. His work often reveals surprising phenomena in higher dimensions, such as the existence of polytopes without rational realizations or with complete graphs.

The recent publications reflect a strong trend in geometric combinatorics, particularly in the study of polytopal structures like associahedra, zonotopes, and hypersimplices, and their combinatorial and algebraic properties. Key themes include universality, realizability, and the interplay between geometry and combinatorics in high-dimensional spaces.

Scientific Awards:

• No specific awards mentioned in the provided text.

Advising and Grants: Arnau Padrol has supervised multiple PhD students and postdoctoral researchers, including Chiara Mantovani, Eva Philippe, Germain Poullot, and Leonardo Martínez-Sandoval. His supervision reflects an active research group in geometric combinatorics. He has been involved in research projects such as Geometry and Algebra in Combinatorics, Red Temática de Matemática Discreta y Algorítmica, Combinatorics and Complexity of Discrete Geometric Structures, and several ANR-funded projects including PAGCAP and CAPPS, indicating sustained grant support for his research.

Labs and Teams: He is a core member of the Combinatorics Research Group at Universitat de Barcelona and is affiliated with IMUB and CRM. At Sorbonne Université, he was part of the Combinatoire et Optimisation team at IMJ-PRG. These affiliations place him within active research networks in discrete mathematics in Europe.