Preprints


  1. The spectrum of the Burnside Tambara functor, with Maxine Elena Calle, David Chan, David Mehrle, Ben Spitz, and Danika Van Niel. arXiv. 
  2. Real syntomic cohomology, with Gabriel Angelini-Knoll and Hana Jia Kong. Submitted. arXiv. 
  3. On the Tambara affine line, with David Chan, David Mehrle, Ben Spitz, and Danika Van Niel. Submitted. arXiv. 
  4. A simple η-torsion family in the stable stems, with Irina Bobkova. Submitted. arXiv. 
  5. Koszul resolutions over incomplete Tambara functors for cyclic p-groups, with David Mehrle and Michael Stahlhauer. Submitted. arXiv. 
  6. New infinite families in the stable homotopy groups of spheres, with Prasit Bhattacharya and Irina Bobkova. Submitted. arXiv.
  7. Bredon homological stability for configuration spaces of G-manifolds, with Eva Belmont and Chase Vogeli. Submitted. arXiv. Video.
  8. Symmetries of exotic spheres via complex and quaternionic Mahowald invariants, with Boris Botvinnik. Submitted. arXiv. Video. 
  9. On the equivalence between two theories of real cyclotomic spectra, with Jay Shah. Submitted. arXiv.


Publications


  1. Pathological computation of Mackey functor-valued Tor over cyclic groups, with David Mehrle and Michael Stahlhauer. To appear in Bull. Lond. Math. Soc. arXiv. 
  2. A motivic analogue of the K(1)-local sphere spectrum, with William Balderrama and Kyle Ormsby. To appear in J. Eur. Math. Soc. arXiv.
  3. Chromatic complexity of the algebraic K-theory of y(n), with Gabriel Angelini-Knoll. J. Pure. Appl. Alg. 229-9 (2025), 108027. arXiv.
  4. The motivic lambda algebra and motivic Hopf invariant one problem, with William Balderrama and Dominic Culver. Geom. Topol. 29-3 (2025), 1489-1570. arXiv. Calculator.
  5. On the parametrized Tate construction, with Jay Shah. J. Topol. 18-1 (2025), e70018. arXiv.
  6. The slice spectral sequence for a motivic analogue of the connective K(1)-local sphere, with Hana Jia Kong. Proc. Lond. Math. Soc. 129-5 (2024), e70006. arXiv.
  7. Some smooth circle and cyclic group actions on exotic spheres. Proc. Amer. Math. Soc. 152 (2024), 1777-1788. arXiv.
  8. The 2-primary Hurewicz image of tmf, with Mark Behrens and Mark Mahowald. Geom. Topol. 27-7 (2023), 2763-2831. arXiv.
  9. 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.
  10. 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.
  11. Tate blueshift and vanishing for Real oriented cohomology, with Guchuan Li and Vitaly Lorman. Adv. Math. 411 (2022), 108780. arXiv. Video.
  12. tmf-based Mahowald invariants. Algebr. Geom. Topol. 22-4 (2022), 1789-1839. arXiv. E8-page of AHSS for C2-Tate of tmf.
  13. Algebraic slice spectral sequences, with Dominic Culver and Hana Jia Kong. Doc. Math. 26 (2021), 1085-1119. arXiv. Slides and video.
  14. Motivic Mahowald invariants over general base fields. Doc. Math. 26 (2021), 561-582. arXiv.
  15. kq-resolutions I, with Dominic Culver. Trans. Amer. Math. Soc. 374-7 (2021), 4655-4710. arXiv.
  16. Real motivic and C2-equivariant Mahowald invariants. J. Topol. 14-2 (2021), 369-418. arXiv.
  17. 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.
  18. The motivic Mahowald invariant. Algebr. Geom. Topol. 19-5 (2019), 2485-2534. arXiv.
  19. 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.
  20. Squares and primitivity in partial words, with F. Blanchet-Sadri, M. Bodnar, J. Nikkel, and X. Zhang. Disc. Appl. Math. 185 (2015), 26-37.
  21. Squares in partial words, with F. Blanchet-Sadri, Y. Jiao, J. M. Machacek, and X. Zhang. Theoret. Comp. Sci. 530 (2014), 42-57.