J.D. Quigley

Email address: jdq27 at cornell dot edu
Office: 580 Malott Hall
CV

I am an H.C. Wang Assistant Professor in the Department of Mathematics at Cornell University. My interests include classical, equivariant, and motivic stable homotopy theory, algebraic K-theory and trace methods, and equivariant algebra.

I also co-organize the Electronic Computational Homotopy Theory seminar with Dan Isaksen and Hana Jia Kong and serve as a Faculty Advisor for the Math Explorers' Club.

Research

• The 2-primary Hurewicz image of tmf, with Mark Behrens and Mark Mahowald. Submitted. Preprint available on arXiv.
• Algebraic slice spectral sequences, with Dominic Culver and Hana Jia Kong. Submitted. Preprint available on arXiv. Slides and video from my talk at the Midwest Topology Seminar.
• tmf-based Mahowald invariants. Submitted. Preprint available on arXiv. E8-page of AHSS for Tate of tmf.
• Tate blueshift and vanishing for Real oriented cohomology, with Guchuan Li and Vitaly Lorman. Submitted. Preprint available on arXiv. Video of my talk from BIRS workshop "Equivariant stable homotopy theory and p-adic Hodge theory".
• On the parametrized Tate construction and two theories of real cyclotomic spectra, with Jay Shah. Submitted. Preprint available on arXiv.
• Chromatic complexity of the algebraic K-theory of y(n), with Gabe Angelini-Knoll. Submitted. Preprint available on arXiv.
• Motivic Mahowald invariants over general base fields. Submitted. Preprint available on arXiv.
• Real motivic and C₂-equivariant Mahowald invariants. Submitted. Preprint available on arXiv
• The Segal Conjecture for topological Hochschild homology of the Ravenel spectra X(n) and T(n), with Gabe Angelini-Knoll. To appear in J. Htpy. Rel. Str. Preprint available on arXiv.
• kq-resolutions I, with Dominic Culver. To appear in Trans. Amer. Math. Soc. Preprint available on arXiv.
• The motivic Mahowald invariant. Alg. Geom. Topol. 19-5 (2019), 2485-2534. Preprint available on arXiv.
• Computing primitively-rooted squares and runs in partial words, with F. Blanchet-Sadri, J. Lazarow, J. Nikkel, and X. Zhang. Eur. J. Comb. 68 (2018), 223-241.
• Squares and primitivity in partial words, with F. Blanchet-Sadri, M. Bodnar, J. Nikkel, and X. Zhang. Disc. Appl. Math. 185 (2015), 26-37.
• Computing primitively-rooted squares and runs in partial words, with F. Blanchet-Sadri, J. Nikkel, and X. Zhang. Combinatorial algorithms, Lecture Notes in Computer Science, Vol. 8986 (2015), 86-97.
• Squares in partial words, with F. Blanchet-Sadri, Y. Jiao, J. M. Machacek, and X. Zhang. Theoret. Comp. Sci. 530 (2014), 42-57.

Teaching