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 and my work draws on modern tools in geometry such as Lie groupoids. My work is currently focused on two areas: generalized complex geometry as it relates to non-commutative geometry and moduli spaces of singular flat connections.

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.

Opening for Graduate students

I’m currently looking to recruit graduate students. Students with a strong interest in geometry and mathematical physics are encouraged to contact me.

Papers and preprints

  1. Jets of foliations and bk-algebroids (with Á. del Pino and A. Witte), arXiv:2311.17045
  2. Castling equivalence for logarithmic flat connections, arXiv:2306.17802
  3. The derived moduli stack of logarithmic flat connections, arXiv:2301.00962
  4. Normal forms and moduli stacks for logarithmic flat connections, arXiv:2209.00631
  5. Brane Quantization of Toric Poisson Varieties (with M. Gualtieri). Commun. Math. Phys. 391, 357–400 (2022), DOI, arXiv version: arXiv:2108.01658
  6. Lie groupoids and logarithmic connections. Sel. Math. New Ser. 30, 44 (2024), DOI, arXiv version: arXiv:2010.03685.
  7. 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
  8. 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

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