One Day, One Family, One Place: Poisson Geometry at CRM

On March 23rd, 2026, the Centre de Recerca Matemàtica hosted the thematic day “Poisson Geometry and Its Relatives”, a full‑day event that brought together researchers exploring Poisson geometry and several of its neighbouring areas. The programme combined classical ideas, new perspectives, and ongoing developments across symplectic geometry, generalized geometry, and higher Lie groupoids.

Morning Sessions: Symmetric Structures and New Perspectives

The day began with F. Moučka (Universitat Autònoma de Barcelona) and his talk “Symmetric cousin of Poisson geometry”.Filip Moučka is a Ph.D. researcher working between the Universitat Autònoma de Barcelona and the Czech Technical University, specializing in differential and generalized geometry, with recent work focused on developing the theory of symmetric Poisson structures. Moučka introduced a symmetric counterpart to classical Poisson geometry, based on symmetric bivector fields paired with torsion-free connections —an alternative framework that mirrors some of the key features of the classical theory while relying on symmetric rather than skew‑symmetric structures. The talk also highlighted connections with well‑known geometric tools and algebraic structures.

M. Crainic during his talk.

After the coffee break, M. Crainic (University of Utrecht) presented “The Lawson-Mitsumatsu symplectic foliation via generalized complex geometry”.Marius Crainic is Professor at Utrecht University, a leading figure in Poisson Geometry and related areas (symplectic and contact, foliations), G-structures, Lie pseudo-groups and groupoids and, more recently, the geometric study of PDEs. His talk revisited a fundamental and still challenging problem: building symplectic foliations of codimension one. By looking at these constructions through the lens of generalized complex geometry, he showed how certain classical results—particularly Mitsumatsu’s construction—can be understood in a more transparent and conceptual way. The talk emphasized how tools from generalized complex geometry shed new light on foundational questions in foliation theory.

Afternoon Sessions: Low‑Regularity Poisson Geometry and Higher Groupoids

In the afternoon, R. Cardona (Universitat de Barcelona – CRM) gave the talk “Towards a C⁰‑Poisson geometry”. Robert Cardona is an assistant professor at the University of Barcelona and a CRM researcher, whose work spans geometry, topology, and dynamical systems. He discussed Poisson homeomorphisms as C⁰-limits of Poisson diffeomorphisms and proposed the first steps toward a theory of “C⁰‑Poisson geometry”. The presentation explored an interplay between flexibility—emerging in low-regularity settings—and rigidity, which persists in the behavior of symplectic foliations and coisotropic submanifolds. Cardona also introduced the idea of “clean intersection points,” a notion relevant both for smooth and singular symplectic foliations.

R. Cardona during his talk

The final talk of the day, “Differentiation and van Est isomorphism for higher Lie groupoids”, was given by A. Cabrera (Universitat Politècnica de Catalunya). Alejandro Cabrera is a differential geometer working on symplectic and Poisson geometry, Lie algebroids, and Lie groupoids, with research bridging pure geometry and mathematical physics, including applications to quantization and geometric mechanics. Cabrera introduced a general procedure to differentiate higher Lie groupoids and simplicial manifolds by considering cochains with higher‑order vanishing on degenerate simplices. This approach extends the classical differentiation of Lie groups and groupoids and leads to a generalized van Est map. The talk concluded with a van Est isomorphism theorem under suitable connectivity conditions and several applications.

A. Cabrera during his talk.

A Day Highlighting the Breadth of Modern Geometry

Poisson Geometry and Its Relatives showcased the richness and diversity of today’s geometric landscape. From new symmetric structures and low‑regularity phenomena to conceptual advances in foliations and the theory of higher groupoids, the event illustrated how active and interconnected these fields are. It was a day that brought together a scientific community to exchange ideas.