research

My research interests include symplectic and Poisson geometry, algebraic topology, geometric quantization, Lie groupoids and differentiable stacks, gerbes, and higher structures in differential geometry.

publications and preprints

• Infinitesimal symmetries of bundle gerbes and Courant algebroids, with D. Djounvouna, Geometriae Dedicata, 218:47 (2024).DOI: https://doi.org/10.1007/s10711-024-00897-0 arXiv:2304.05347
• Sheaves, principal bundles, and Čech cohomology for diffeological spaces, with J. Watts and S. Wolbert, 28 pages. Accepted for publication in Israel Journal of Mathematics (2023). arXiv:2111.01032
• Multiplicative vector fields on bundle gerbes, with J. Vaughan, Differential Geometry and its Applications, 84 (2022), 31 pages. DOI: https://doi.org/10.1016/j.difgeo.2022.101931. arXiv:2003.12874
  (Watch a talk on this topic here.)
• Basic equivariant gerbes on non-simply connected compact simple Lie groups, Journal of Geometry and Physics, 133 (2018), pp. 30-41. DOI: https://doi.org/10.1016/j.geomphys.2018.06.016. arXiv:1712.08294
• Differential cocycles and Dixmier-Douady bundles, with J. Watts, Journal of Geometry and Physics, 130 (2018), pp. 168-183. DOI: https://doi.org/10.1016/j.geomphys.2018.01.028. arXiv:1705.01162
• Groupoid equivariant prequantization, Communications in Mathematical Physics, 360, no. 1 (2018), pp. 169-195. DOI: https://doi.org/10.1007/s00220-017-3080-x. arXiv:1611.04711
• Prequantization of the moduli space of flat PU(p) bundles with prescribed boundary holonomies, Symmetry, Integrability and Geometry: Methods and Applications (Special issue on Poisson Geometry in Mathematics and Physics), 10 (2014), 109, 13 pages. arXiv:1408:0253
• Inertia groups of a toric DM stack, fake weighted projective stacks, and labelled sheared simplices, with R. Goldin, M. Harada, D. Johannsen. Rocky Mountain Journal of Mathematics, 46, no. 2 (2016), pp. 481-517. arxiv:1306.5036
• Global quotients among smooth toric DM stacks, with M. Harada. Osaka Journal of Mathematics, 52, no. 1 (2014), pp. 236-269. arXiv:1302.0385
• On the Verlinde formulas for SO(3), with E. Meinrenken. Quarterly Journal of Mathematics, 64, no. 1 (2013), pp. 235-252. arXiv:1106.4854
• Quantization of the moduli space of flat G-bundles using G-valued moment maps, Oberwolfach Reports, 9 (2011), pp. 469-470.
• Central extensions of loop groups and obstruction to prequantization, Canadian Mathematical Bulletin, 56 (2013), pp. 116-126. arXiv:1004.2278
• Prequantization of the moduli space of flat G-bundles over a surface, Journal of Geometry and Physics, 58, no. 11 (2008), pp. 1624-1637. arXiv:0708.1269

thesis

Pre-quantization of the moduli space of flat G-bundles. (pdf file)
Ph. D. Thesis supervised by Eckhard Meinenken and Paul Selick, University of Toronto (2009).