Research Week Showcase: Dr. Francis Bischoff
For the UofR’s Research Week, the Department of Mathematics and Statistics is excited to showcase Dr. Francis Bischoff and his research as an NSERC Discovery Grant 2024 recipient!
Dr. Francis Bischoff is an Assistant Professor in the Department of Mathematics and Statistics at the University of Regina. He completed his Ph.D. in Mathematics from the University of Toronto in 2019 under the supervision of Dr. Marco Gualtieri. He joined the University of Regina in 2023, and he has been a valued member of the Regina Topology and Geometry group since his arrival.
Dr. Bischoff’s research interests lie at the intersection of complex algebraic geometry, Poisson geometry, and theoretical physics. In his PhD thesis, he worked on a problem in generalized complex geometry, which is a kind of geometry that originated from the study of supersymmetric quantum field theories. This geometry encompasses complex and symplectic geometry into a unified framework, and his work in this area has found applications in the study of non-commutative geometry. More recently, a major theme in his research has been the geometric study of differential equations. Using connections (or first-order differential equations on a smooth manifold), paths, surfaces and higher dimensional membranes within a manifold can be represented as the symmetries of a vector space. As a result, there is a close relationship between the topology of a manifold and the possible connections which can be defined on it. Several of his recent research activities have exploited this deep relationship between geometry and calculus. Currently, Dr. Bischoff’s research team includes undergraduate and graduate students such as Aditya Dwarkesh (Ph.D. student), Shane J. Crerar (M.Sc. student), and Cody Antal (NSERC USRA summer student).
Outside of his research, Dr. Bischoff writes his own math blog where he discusses interesting topics in the fields of geometry and topology. These discussions range from intermediate topics like the encoding of a space using a Lie algebra to more complex topics such as Deligne’s construction of a flat logarithmic vector bundle. In addition, he was an avid skateboarder in his youth who has been featured in skater magazines!
For any students, faculty members, or researchers who are interested in learning more about Dr. Bischoff and his research activities, please see his website or contact him via email at francis.bischoff@uregina.ca.