Email address: uerbum@impa.br, verbum@ciencias.unam.mx,
Bio/ Research interests
I am a postdoctoral fellow at IMPA. My research lies at the interface of Poisson geometry, generalized geometry and mathematical physics. In particular, I use ideas from Chern-Simons theory and higher symplectic geometry to study Courant algebroids and generalized Kähler manifolds. I earned my PhD at IMPA under the supervision of Henrique Bursztyn. I subsequently held positions as a lecturer at UNAM (2020-2021) and a Postdoctoral Fellow at the University of Toronto (2021-2024). In 2026, I received the André Lichnerowicz Prize in Poisson Geometry.
Symplectic double groupoids and the generalized Kähler potential (with Marco Gualtieri and Yucong Jiang).
Separates the holomorphic data of a generalized Kähler structure from its metric using symplectic double groupoids and Lagrangian bisections, establishing the existence of generalized Kähler potentials.
Poisson groupoids and moduli spaces of flat bundles over surfaces [Adv. Math. 440 (2024), Paper no. 109523]
Constructs Poisson and symplectic groupoid structures on decorated moduli spaces of flat bundles using surface gluing and Lie 2-groups.
Transitive Courant algebroids and double symplectic groupoids [Int. Math. Res. Not. IMRN (2024), no. 9, 7526-7551]
Extends the Lu–Weinstein construction to Lie bialgebroids with transitive Courant doubles and integrable underlying Atiyah algebroids.
Shifted lagrangian structures in Poisson geometry (with Henrique Bursztyn and Miquel Cueca)
Uses 2-shifted lagrangian morphisms to integrate quasi-Poisson manifolds and construct quasi-symplectic groupoids.
Morita equivalences, moduli spaces and flag varieties [Int. Math. Res. Not. IMRN (2026), no. 5, rnag039]
Realizes configuration Poisson groupoids of flags as decorated moduli spaces of flat bundles and constructs integrations for them which are symplectically Morita equivalent.
Morphisms of double Lie groupoids: a simplicial approach (with Kalin Krishna and Stefano Ronchi) Develops a simplicial framework for morphisms of double Lie groupoids, with applications to nonabelian gerbes and the integration of Courant algebroids.
Homological vector fields over differentiable stacks (with Miquel Cueca). Introduces homological vector fields up to homotopy on graded groupoids, providing a Morita-invariant framework for Lie and Courant algebroids over differentiable stacks
Reduction of symplectic groupoids and quotients of quasi-Poisson manifolds [Transform. Groups, Vol. 28, no. 4, 1357-1374, (2023)] Develops a common framework for integrating quasi-Poisson quotients through symplectic groupoid reduction, with applications to double symplectic groupoids.
Complete Lie algebroid actions and the integrability of Lie algebroids [Proc. Amer. Math. Soc., 149 (2021), 4923-4930] Gives a new proof that a Lie algebroid is integrable exactly when it admits a complete action on a surjective submersion.
Integrability of quotients in Poisson and Dirac geometry [Pacific J. Math., 311-1 (2021), pp. 1-32] Establishes integrability results for quotient Poisson and Dirac structures, including explicit groupoid integrations of Poisson and Dirac homogeneous spaces.
Leaves of stacky Lie algebroids [C. R. Math. Acad. Sci. Paris, Volume 358 (2020) no. 2, pp. 217-226] Studies groupoid structures on leaves of LA-groupoids meeting the unit manifold, obtaining symplectic groupoids from the symplectic leaves of Poisson groupoids.
Integration of action Courant algebroids (with Marco Gualtieri)
Poisson manifolds of complex reductive type (with Maarten Mol)
Slides from some talks (some recordings on Youtube)
Global aspects of quasi-Poisson geometry
Geometría Kähler generalizada y geometría de Poisson (spanish)
2-shifted lagrangian groupoids in Poisson geometry
On the integration of Lie bialgebroids
Symplectic double groupoids and the generalised Kähler potential (these contain really nice art!)