Research
I am fascinated by symmetry and the surprisingly elegant way in which it pops up in (symplectic and Poisson) geometry and quantum theory. On a technical level, this translates into a fairly broad spectrum of research interests lying in the intersection of Differential Geometry, Topology, and Mathematical Physics. At the moment, my research centers around certain infinite-dimensional Lie algebras that are intimately related to time-dependent (classical) mechanics and the implications of their having integrating objects with "compactness" properties. I am also working on extending the cohomology and van Est theory of Lie groups and Lie algebras to the (categorical) realm of Lie 2-groups and Lie 2-algebras with an eye out for applications to integrability.
Multiplicative Gray stability (with María Amelia Salazar and Daniele Sepe)
A cohomological proof for the integrability of strict Lie 2-algebras, IJGMMP, Vol. 19, No. 14, 2250222 (2022)
Towards a new cohomology theory for strict Lie 2-groups
A new cohomology theory for strict Lie 2-algebras, Commun. Contemp. Math., Vol. 24, No. 3, 2150017 (2022)
On the existence of certain axisymmetric interior metrics (with Davide Batic and Marek Nowakowski), J. Math. Phys. 51, 082504 (2010)
Upcoming projects
The van Est isomorphism and the Weil algebra of a strict Lie 2-algebra (with Miquel Cueca Ten).
Local normal forms for Jacobi manifolds of compact type (with María Amelia Salazar and Daniele Sepe).
Other notes
In August 2022, prior to my appointment, I gave a minicourse on Poisson geometry at Jilin University. Here are the slides.
In Spring 2016, we organized a seminar on stacks. Here are some notes.
Here are some notes I wrote on the Kodaira vanishing theorem.