About me

My name is Francis Bischoff. I am an Assistant Professor in the Department of Mathematics & Statistics at the University of Regina, where I am part of the Topology and Geometry group.

My research interests lie at the intersection of complex algebraic geometry, Poisson geometry, and theoretical physics. I have worked on generalized complex geometry and its relation to non-commutative geometry, as well as on moduli spaces of singular flat connections and various related geometric structures. More recently, I have focused on higher categorical connections and the surface signature.

Video recordings for many of my talks are available on Youtube. I also have some expository writings on this page, on Twitter (with some ‘unrolled’ threads here) and on Mathstodon.

Before taking up my current position, I was a Junior Research Fellow at Exeter College and the University of Oxford and briefly a postdoctoral fellow at the Fields Institute during the thematic program on Homological Algebra of Mirror Symmetry. I completed a Master’s degree (2014) and a Ph.D. (2019) in Mathematics at the University of Toronto, under the supervision of Marco Gualtieri. 

In my thesis, I developed a new approach to generalized Kähler geometry based on holomorphic symplectic Morita equivalences and I applied this to solve the problem of describing the metric of a generalized Kähler structure of symplectic type in terms of a single potential function. I have written a brief summary of this work here.

Papers and preprints

  1. bk-algebroids and the variety of foliation jets (with Á. del Pino and A. Witte), arXiv:2508.20241
  2. Thin homotopy and the signature of piecewise linear surfaces (with D. Lee), arXiv:2506.16657
  3. Jets of foliations and bk-algebroids (with Á. del Pino and A. Witte), arXiv:2311.17045
  4. Castling equivalence for logarithmic flat connections, arXiv:2306.17802
  5. The derived moduli stack of logarithmic flat connections, arXiv:2301.00962
  6. Normal forms and moduli stacks for logarithmic flat connections. J. Algebraic Geom. 34, 331-379 (2025), DOI, arXiv version: arXiv:2209.00631
  7. Brane Quantization of Toric Poisson Varieties (with M. Gualtieri). Commun. Math. Phys. 391, 357–400 (2022), DOI, arXiv version: arXiv:2108.01658
  8. Lie groupoids and logarithmic connections. Sel. Math. New Ser. 30, 44 (2024), DOI, arXiv version: arXiv:2010.03685.
  9. Deformation spaces and normal forms around transversals (with H. Bursztyn, H. Lima and E. Meinrenken). Compos. Math, 156, 697-732 (2020), DOI, arXiv version: arXiv:1807.11153
  10. Morita equivalence and the generalized Kähler potential (with M. Gualtieri and M. Zabzine), J. Differential Geom. 121.2, 187-226 (2022), DOI, arXiv version: arXiv:1804.05412

Leave a comment