**Email address:** jquigley1993 at gmail dot com

CV

I am an algebraic topologist interested in homotopy theory and its applications in geometry, topology, and algebra. I am a postdoc at the University of Oregon.

I also co-organize the Electronic Computational Homotopy Theory online research community and the UO Topology Seminar.

**v**, with Hana Jia Kong. Submitted. arXiv._{1}-periodic motivic homotopy over prime fields**Some smooth circle and cyclic group actions on exotic spheres**. Submitted. arXiv.**The motivic lambda algebra and motivic Hopf invariant one problem**, with William Balderrama and Dominic Culver. Submitted. arXiv. Calculator.**On the equivalence between two theories of real cyclotomic spectra**, with Jay Shah. Submitted. arXiv.**On the parametrized Tate construction**, with Jay Shah. Submitted. arXiv.**Chromatic complexity of the algebraic K-theory of y(n)**, with Gabriel Angelini-Knoll. Submitted. arXiv.**Ranks of RO(G)-graded stable homotopy groups of spheres for finite groups G**, with J.P.C. Greenlees. To appear in*Proc. Amer. Math. Soc., Ser. B.*arXiv.**The 2-primary Hurewicz image of tmf**, with Mark Behrens and Mark Mahowald. To appear in*Geom. Topol.*arXiv.**Free incomplete Tambara functors are almost never flat**, with Mike Hill and David Mehrle. To appear in*Int. Math. Res. Notices*arXiv. Video.**Tate blueshift and vanishing for Real oriented cohomology**, with Guchuan Li and Vitaly Lorman.*Adv. Math.*411 (2022), 108780. arXiv. Video.**tmf-based Mahowald invariants**.*Algebr. Geom. Topol.*22-4 (2022), 1789-1839. arXiv. E8-page of AHSS for C_{2}-Tate of tmf.**Algebraic slice spectral sequences**, with Dominic Culver and Hana Jia Kong.*Doc. Math.*26 (2021), 1085-1119. arXiv. Slides and video.**Motivic Mahowald invariants over general base fields**.*Doc. Math.*26 (2021), 561-582. arXiv.**kq-resolutions I**, with Dominic Culver.*Trans. Amer. Math. Soc.*374-7 (2021), 4655-4710. arXiv.**Real motivic and C**._{2}-equivariant Mahowald invariants*J. Topol.*14-2 (2021), 369-418. arXiv.**The Segal Conjecture for topological Hochschild homology of the Ravenel spectra**, with Gabriel Angelini-Knoll.*J. Htpy. Rel. Str.*16-1 (2021), 41-60. arXiv.**The motivic Mahowald invariant**.*Algebr. Geom. Topol.*19-5 (2019), 2485-2534. 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. -
**Squares in partial words**, with F. Blanchet-Sadri, Y. Jiao, J. M. Machacek, and X. Zhang.*Theoret. Comp. Sci.*530 (2014), 42-57.