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Blog Post number 4
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Blog Post number 1
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portfolio
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publications
The Jacobi morphism and the Hessian in higher order field theory; with applications to a Yang-Mills theory on a Minkowskian background
(with Marcella Palese)
Int. Jour. Geom. Meth. Mod. Phys. (2020) 2050114
Symmetry transformations of extremals and higher conserved quantities: invariant Yang–Mills connections
(with Marcella Palese)
J. Math. Phys. 62, 043504 (2021)
Haefliger’s differentiable cohomology
(with Marius Crainic)
Journal of Noncommutative Geometry (2023), accepted
A groupoid approach to transitive differential geometry
(with Francesco Cattafi)
Pseudogroups of symmetries and Morita equivalences
(with Francesco Cattafi)
Pseudogroups and geometric structures
(with Francesco Cattafi, Marius Crainic, and María Amelia Salazar)
This is a book describing a modern approach to the theory of Lie pseudogroups and geometric structure on manifolds that builds upon the theory of Lie groupoids, principal groupoid actions, and multiplicative structures. The main achievements include a clarification of the foundations of Élie Cartan’s work on the subject and a framework capable of dealing with non transitive pseudogroups.
Horizontal Morse Theory
(with Fabio Gironella, Álvaro del Pino Gómez, and Lauran Toussaint)
This paper develops a version of Morse theory compatible with a codimension one distribution on a manifold.
seminars
Exterior Differential Systems
Published:
Local reading seminar co-organized with Francesco Cattafi at Universiteit Utrecht, and based on the classical sources by Robert Bryant.
Equivariant cohomology
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Local reading seminar co-organized with Maarten Mol and Sergej Monavari at Universiteit Utrecht. We started from the classical paper by Atiyah and Bott on the subject, and moved to various related topics.
Poisson seminars
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I was coordinator, together with Karandeep Singh, of the seminar of the symplectic geometry section at KU Leuven.
Pure and Applied Differential Geometry - PADGE
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The PADGE conferences are organized by the KU Leuven Geometry Section approximately every five years and are dedicated to the memory of Franki Dillen (1963-2013).
talks
Geometric structures via Pfaffian groupoids
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Cohomology of Haefliger groupoids and characteristic invariants of pseudogroup structures
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Morse theory along bracket generating distributions
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Haefliger’s differentiable cohomology
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Symmetries and cohomological invariants in differential geometry - a Lie groupoid approach
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Cartan geometries and Lie groupoids II
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Jacobi geometry and deformations of foliations
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Natural bundles as actions of étale stacks
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Chern-Weil characteristic classes for principal groupoid bundles (poster presentation)
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teaching
Bachelor level TA
Teaching assistant, Universiteit Utrecht, 2017
Poisson geometry
Exercise class, Universiteit Utrecht, 2019
Morse theory and the h-cobordism theorem
Master seminar in differential geometry, Universiteit Utrecht, 2020
Lie algebras with a nice basis
Second reader Master thesis, KU Leuven, 2023