Research

My research is in algebraic topology. I work in equivariant homotopy theory with a focus on RO(G)-graded Bredon cohomology, structured ring spectra, parametrized cohomology, tensor triangular geometry, and representation theory.

Click here for a brief introduction to RO(C₂)-graded cohomology.

Course page and videos for a graduate topics course on spectral sequences I taught at UCLA in Spring 2020.

A wealth of resources for homotopy theory and K-theory compiled by Blumberg, Bohmann, Gerhardt, Hill, Malkiewich, Mandell, Merling, Ponto, and Zakharevich.

Preprints

• Equivariant H𝔽_p-modules are wild
  Joint with Jacob Fjeld Grevstad.
  arXiv preprint
  
  

Publications

• A guide to equivariant parametrized cohomology
  Topology and its Applications 376 (2025) 109449.
  Joint with Agnès Beaudry, Chloe Lewis, Sabrina Pauli, and Elizabeth Tatum.
  arXiv preprint, Published version

• Equivariant Z/ℓ-modules for the cyclic group C₂
  Journal of Pure and Applied Algebra 228, 3 (2024), 107473.
  Joint with Daniel Dugger and Christy Hazel.
  arXiv preprint, Published version

• Genuine-commutative structure on rational equivariant K-theory for finite abelian groups
  Bulletin of the London Mathematical Society 54 (2022).
  Joint with Anna Marie Bohmann, Christy Hazel, Jocelyne Ishak, and Magdalena Kedziorek.
  arXiv preprint, Published version
  

• Naive-commutative structure on rational equivariant K-theory for abelian groups
  Topology and its Applications 316 (2022), 108100.
  Joint with Anna Marie Bohmann, Christy Hazel, Jocelyne Ishak, and Magdalena Kedziorek.
  arXiv preprint, Published version
  

• The freeness theorem for equivariant cohomology of Rep(C₂)-complexes
  Topology and its Applications 285 (2020), 107413.
  Joint with Eric Hogle.
  arXiv preprint, Published version

• A structure theorem for RO(C₂)-graded cohomology
  Algebraic & Geometric Topology 20-4 (2020), 1691--1728.
  arXiv preprint, Published version