Research

Broadly, my research is in the areas of differential geometry, mathematical physics, and topology. 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. More recently, I have been studying topological quantum field theories taking values in categories of spans and relations.

Preprints

  1. 2-Segal sets and pseudomonoids in the bicategory of spans (with S. Marx)
  2. Graded geometry and generalized reduction (with H. Bursztyn, A. Cattaneo, and M. Zambon)

Publications

* indicates undergraduate or postbaccalaureate student coauthor

  1. A geometric characterization of N-graded manifolds and the Frobenius theorem (with H. Bursztyn and M. Cueca), Journal of Noncommutative Geometry (2025).
  2. Frobenius and commutative pseudomonoids in the bicategory of spans (with I. Contreras and W. Stern), Journal of Geometry and Physics 207 (2025), 105309.
  3. On Examples and Classification of Frobenius Objects in Rel (with I. Contreras, A. Long*, and S. Marx*), Contemporary Mathematics 802 (2024), 75-92.
  4. Modules and representations up to homotopy of Lie n-algebroids (with M. Jotz Lean and T. Papantonis), Journal of Homotopy and Related Structures 18 (2023), 23-70.
  5. Frobenius objects in the category of spans (with I. Contreras and M. Keller*), Review in Mathematical Physics 34 (2022), no. 10, 2250036.
  6. Courant cohomology, Cartan calculus, connections, curvature, characteristic classes (with M. Cueca), Communications in Mathematical Physics 381 (2021), 1091-1113.
  7. Frobenius objects in the category of relations (with R. Zhang*), Letters in Mathematical Physics 110 (2020), no. 7, 1941-1959.
  8. 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.
  9. Constant symplectic 2-groupoids (with X. Tang), Letters in Mathematical Physics 108 (2018), no. 5, 1203-1223.
  10. Symplectic structures on the integration of exact Courant algebroids (with X. Tang), Journal of Geometry and Physics 127 (2018), 68-83.
  11. VB-groupoids and representation theory of Lie groupoids (with A. Gracia-Saz), Journal of Symplectic Geometry 15 (2017), no. 3, 741-783.
  12. Modular classes of Lie groupoid representations up to homotopy, SIGMA 11 (2015), 058, 10 pages.
  13. The Atiyah class of a dg-vector bundle (with M. Stiénon and P. Xu), Comptes Rendus Mathématique 353 (2015), no. 4, 357-362.
  14. Lie algebroid modules and representations up to homotopy, Indagationes Mathematicae 25 (2014), 1122-1134.
  15. Differential graded contact geometry and Jacobi structures, Letters in Mathematical Physics 103 (2013), 729-741.
  16. L-infinity algebra actions (with M. Zambon), Differential Geometry and its Applications 30 (2012), 576-587.
  17. From double Lie groupoids to local Lie 2-groupoids (with X. Tang), Bulletin of the Brazilian Mathematical Society 42 (2011), no. 4, 651-681.
  18. On homotopy Poisson actions and reduction of symplectic Q-manifolds, Differential Geometry and its Applications 29 (2011), 319-328.
  19. 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.
  20. Q-algebroids and their cohomology, Journal of Symplectic Geometry 7 (2009), no. 3, 263-293.
  21. Q-groupoids and their cohomology, Pacific Journal of Mathematics 242 (2009), no. 2, 311-332.
  22. Supergroupoids, double structures, and equivariant cohomology, UC Berkeley Ph.D. thesis.

Slides/video/notes from some talks