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J.D. Quigley

H.C. Wang Assistant Professor

Image of J.D. Quigley

Malott Hall, Room 580

Educational Background

  • Ph.D. (2019) University of Notre Dame



  • Mathematics


Algebraic topology and K-theory
I am interested in algebraic topology and especially the computation of the stable homotopy groups of spheres. Spheres have interesting properties, such as reflectional symmetry or algebraic structure, which can be leveraged to simplify many calculations. My primary goal is incorporating these properties into existing tools from stable homotopy theory. I am particularly interested in the case of K-theory, where the classical theory (topological K-theory) is well-understood but its equivariant analogs (equivariant and Real K-theory) and motivic analogs (algebraic and hermitian K-theory) are more mysterious.


Fall 2020


  • The motivic Mahowald invariant, to appear in Algebraic & Geometric Topology. arXiv:1801.06035.
  • The Segal Conjecture for topological Hochschild homology of the Ravenel spectra X(n) and T(n), (with Gabe Angelini-Knoll) (2017). arXiv:1705.03343.
  • Real motivic and $C_2$-equivariant Mahowald invariants, (2019). arXiv:1904.12996.
  • Motivic Mahowald invariants over general base fields, (2019). arXiv:1905.03902.
  • Complex motivic kq-resolutions, with Dominic Culver (2019). arXiv:1905.11952.