Research

• On the Tambara affine line, with David Chan, David Mehrle, Ben Spitz, and Danika Van Niel. Submitted. arXiv. 
• A simple η-torsion family in the stable stems, with Irina Bobkova. Submitted. arXiv. 
• Pathological computation of Mackey functor-valued Tor over cyclic groups, with David Mehrle and Michael Stahlhauer. Submitted. arXiv. 
• Koszul resolutions over incomplete Tambara functors for cyclic p-groups, with David Mehrle and Michael Stahlhauer. Submitted. arXiv. 
• New infinite families in the stable homotopy groups of spheres, with Prasit Bhattacharya and Irina Bobkova. Submitted. arXiv.
• Bredon homological stability for configuration spaces of G-manifolds, with Eva Belmont and Chase Vogeli. Submitted. arXiv. Video.
• Symmetries of exotic spheres via complex and quaternionic Mahowald invariants, with Boris Botvinnik. Submitted. arXiv.
• 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.
• The slice spectral sequence for a motivic analogue of the connective K(1)-local sphere, with Hana Jia Kong. To appear in Proc. Lond. Math. Soc. arXiv.
• A motivic analogue of the K(1)-local sphere spectrum, with William Balderrama and Kyle Ormsby. To appear in J. Eur. Math. Soc. arXiv.
• The motivic lambda algebra and motivic Hopf invariant one problem, with William Balderrama and Dominic Culver. To appear in Geom. Topol. arXiv. Calculator.
• Some smooth circle and cyclic group actions on exotic spheres. Proc. Amer. Math. Soc. 152 (2024), 1777-1788. arXiv.
• The 2-primary Hurewicz image of tmf, with Mark Behrens and Mark Mahowald. Geom. Topol. 27-7 (2023), 2763-2831. arXiv.
• Ranks of RO(G)-graded stable homotopy groups of spheres for finite groups G, with J.P.C. Greenlees. Proc. Amer. Math. Soc. Ser. B. 10 (2023), 101-113. arXiv.
• Free incomplete Tambara functors are almost never flat, with Mike Hill and David Mehrle. Int. Math. Res. Notices 2023-5 (2023), 4225-4291. 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 C₂-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 C₂-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.