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. 

Publications and preprints (You can also go to my Google Scholar)

1.  The van Est homomorphism for strict Lie 2-groups (with Miquel Cueca), 

      arXiv:2405.09969. 

2.  Multiplicative Gray stability (with María Amelia Salazar and Daniele Sepe), Awaiting for publication on Journal of Symplectic Geometry (2024) 

      arXiv:2109.08542. 

3.  A cohomological proof for the integrability of strict Lie 2-algebras, IJGMMP, Vol. 19, No. 14, 2250222 (2022) 

      arXiv:2103.05414.

4.  Towards a new cohomology theory for strict Lie 2-groups, Theory and Applications of Categories, Vol. 41, 2024, No. 19, pp 593-666.

      arXiv:2103.05412.

5.  A new cohomology theory for strict Lie 2-algebras, Commun. Contemp. Math., Vol. 24, No. 3, 2150017 (2022) 

     arXiv:1811.03876.

6.  On the existence of certain axisymmetric interior metrics (with Davide Batic and Marek Nowakowski), J. Math. Phys.  51, 082504 (2010)

          arXiv:1007.4525.

Upcoming projects

Local normal forms for Jacobi manifolds of compact type (with María Amelia Salazar and Daniele Sepe).

Remarks on the integrability of LA-groupoids over groups.

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.