Site Header — ASOIU Mathematics Research Center
Mathematics Research Center
Keegan Flood — Mathematics Research Center
K.F.
Researcher
Keegan Flood
Geometry Research Group

I am interested in noncommutative geometry, geometric analysis, Cartan geometry, and geometric topology. My primary focus is the extension of classical differential geometric constructions (e.g. jets, differential operators, differential equations, higher order connections, Moyal quantization, multivector fields, Poisson geometry, etc.) to the noncommutative setting of unital associative algebras equipped with some additional structure encoding a notion of ‘‘geometry”.

Noncommutative geometry Jet functors Differential operators Principal symbols Parabolic geometry Projective differential geometry c-projective geometry Geometric analysis Hopf algebras Lagrangian contact geometry BGG sequences Tractor calculus
  • 2026 – present Researcher, Mathematics Research Center
    ASOIU, Baku, Azerbaijan
  • 2023 – 2025 Postdoctoral Researcher, Faculty of Mathematics and Computer Science
    UniDistance Suisse, Brig, Switzerland
  • 2020 – 2023 Postdoctoral Researcher, Department of Mathematics and Statistics
    Masaryk University, Brno, Czech Republic
  • 2019 Ph.D. in Mathematics, University of Auckland, New Zealand
    Supervisors: A. Rod Gover and Pedram Hekmati
    Thesis: The geometry of solutions to the metrizability equation in projective and c-projective geometry
  • 2014 M.Math. in Pure Mathematics, University of Waterloo, Canada
    Supervisors: Alexandru Nica
    Thesis: Brownian motion and the Dirichlet problem
  • 2013 B.Sc. in Mathematics, University of Washington, Seattle, USA
  • Canonical differential calculi via functorial geometrization
    with Gabriele Lobbia and Giacomo Tendas
    preprint (2025)
  • Higher order connections in noncommutative geometry
    with Mauro Mantegazza and Henrik Winther
    preprint (2025)
  • Symbols in noncommutative geometry
    with Mauro Mantegazza and Henrik Winther
    preprint (2025)
  • Flat extensions of principal connections and the Chern–Simons 3-form
    with Andreas Čap and Thomas Mettler
    Annales Henri Lebesgue 8 (2025), 1037–1059
  • Jet functors in noncommutative geometry
    with Mauro Mantegazza and Henrik Winther
    Selecta Mathematica New Series 31, 70 (2025)
  • Canonical curves and Kropina metrics in Lagrangian contact geometry
    with Tianyu Ma, Vladimir Matveev, and Vojtěch Žádník
    Nonlinearity 37 (2024), 015007
  • Geometry of solutions to the c-projective metrizability equation
    with A. Rod Gover
    Annali di Matematica Pura ed Applicata 202 (2023), 1343–1368
  • Metrics in projective differential geometry: the geometry of solutions to the metrizability equation
    with A. Rod Gover
    Journal of Geometric Analysis 29(3) (2019), 2492–2525
  • Constructing canonical calculi
    A Quantum of Noncommutativity Ambleside, United Kingdom, 8 July 2025
  • Constructing canonical calculi
    Differential Geometry and its Applications. Brno, Czech Republic, 13 September 2025
  • Spencer operators and higher connections in the noncommutative setting
    Srní Winter School, Geometry and Physics — Srní, Czech Republic, January 2024
  • Principal symbols in noncommutative geometry
    Workshop on Noncommutative and Generalized Geometry in String Theory, Gauge Theory and Related Physical Models — Corfu, Greece, September 2023
  • Principal symbols in noncommutative geometry
    Quantum Groups and Noncommutative Geometry in Prague — Prague, Czech Republic, September 2023
  • Jet functors and differential operators in noncommutative geometry
    Emergent Geometries from Strings and Quantum Fields — Florence, Italy, July 2023
  • The jet functor in noncommutative geometry
    Srní Winter School, Geometry and Physics — Srní, Czech Republic, January 2022
  • C-projectively compact quasi-Kähler metrics with CR boundary
    Connections, Symmetries, and Finsler Geometry Conference — Universität Jena, Germany, November 2020
  • The geometry of singular solutions to the c-projective metrizability equation
    Differential Geometry Seminar, Masaryk University — Brno, Czech Republic, October 2020
  • C-projective metrizability and CR submanifolds
    Analysis Seminar, University of California San Diego — May 2019
  • Non-normal BGG equations and curved orbit decompositions
    Australian Mathematical Society Annual Conference — University of Adelaide, December 2018
  • Scalar curvature and projective compactification
    Geometry Seminar, KU Leuven — Leuven, Belgium, November 2018
  • Scalar curvature and projective compactification
    Sophus Lie Seminar, University of Tromsø — Norway, November 2018
  • Conformal geometry via tractor calculus
    Sophus Lie Seminar, University of Tromsø — Norway, November 2018
  • Scalar curvature and projective compactification
    Geometric Analysis Seminar, Goethe Universität Frankfurt — Germany, November 2018
  • Metric projective geometries and projective compactification
    Differential Geometry, Lie Theory, and Low-Dimensional Topology — La Trobe University, Melbourne, December 2016