Research

My research is in the broad areas of differential geometry and mathematical physics. Specifically, my work deals with Lie groupoids, Lie algebroids, symplectic geometry, Poisson geometry, and generalized geometry, often using the methods of differential graded geometry and higher category theory.

• Preprint versions of my published papers since 2013 are available through Smith ScholarWorks.
• Preprint versions of all my papers are available on the arXiv.
• My Google Scholar profile has (approximate) citation counts.
• My ORCID profile

Preprints

1. On Examples and Classification of Frobenius Objects in Rel (with I. Contreras, A. Long, and S. Marx), submitted.
2. Modules and representations up to homotopy of Lie n-algebroids (with M. Jotz Lean and T. Papantonis), submitted.

Publications

* indicates undergraduate student coauthor

1. Frobenius objects in the category of spans (with I. Contreras and M. Keller*), Review in Mathematical Physics (2022).
2. Courant cohomology, Cartan calculus, connections, curvature, characteristic classes (with M. Cueca), Communications in Mathematical Physics 381 (2021), 1091-1113.
3. Frobenius objects in the category of relations (with R. Zhang*), Letters in Mathematical Physics 110 (2020), no. 7, 1941-1959.
4. Double Lie algebroids and representations up to homotopy (with A. Gracia-Saz, M. Jotz Lean, and K. C. H. Mackenzie), Journal of Homotopy and Related Structures 13 (2018), no. 2, 287-319.
5. Constant symplectic 2-groupoids (with X. Tang), Letters in Mathematical Physics 108 (2018), no. 5, 1203-1223.
6. Symplectic structures on the integration of exact Courant algebroids (with X. Tang), Journal of Geometry and Physics 127 (2018), 68-83.
7. VB-groupoids and representation theory of Lie groupoids (with A. Gracia-Saz), Journal of Symplectic Geometry 15 (2017), no. 3, 741-783.
8. Modular classes of Lie groupoid representations up to homotopy, SIGMA 11 (2015), 058, 10 pages.
9. The Atiyah class of a dg-vector bundle (with M. Stiénon and P. Xu), Comptes Rendus Mathématique 353 (2015), no. 4, 357-362.
10. Lie algebroid modules and representations up to homotopy, Indagationes Mathematicae 25 (2014), 1122-1134.
11. Differential graded contact geometry and Jacobi structures, Letters in Mathematical Physics 103 (2013), 729-741.
12. L-infinity algebra actions (with M. Zambon), Differential Geometry and its Applications 30 (2012), 576-587.
13. From double Lie groupoids to local Lie 2-groupoids (with X. Tang), Bulletin of the Brazilian Mathematical Society 42 (2011), no. 4, 651-681.
14. On homotopy Poisson actions and reduction of symplectic Q-manifolds, Differential Geometry and its Applications 29 (2011), 319-328.
15. Lie algebroid structures on double vector bundles and representation theory of Lie algebroids (with A. Gracia-Saz), Advances in Mathematics 223 (2010), no. 4, 1236-1275.
16. Q-algebroids and their cohomology, Journal of Symplectic Geometry 7 (2009), no. 3, 263-293.
17. Q-groupoids and their cohomology, Pacific Journal of Mathematics 242 (2009), no. 2, 311-332.
18. Supergroupoids, double structures, and equivariant cohomology, UC Berkeley Ph.D. thesis.

Slides/video/notes from some talks

• Frobenius objects in Rel and Span, June 2022 poster at Banff International Research Station
• Courant cohomology and Cartan calculus, December 2019 talk at Instituto de Matematica Pura e Aplicada, video here
• Constant symplectic 2-groupoids, April 2017 talk at Banff International Research Station, video here
• Representing representations up to homotopy
• Notes on Integration of DG symplectic manifolds via mapping spaces
• Integrating exact Courant algebroids
• Differential graded contact geometry
• Symplectic 2-groupoids and Courant algebroids (video from talk at Poisson 2012)
• Mathematics of the Falling Cat (Survey talk aimed at undergraduates, primarily based on a paper by Richard Montgomery)
• Double Lie groupoids, Lie 2-groupoids, and integration of Courant algebroids
• The fundamental group(oid) of a Lie groupoid
• Homotopy Poisson actions