Papers

Pre-prints:

  1. Essential dimension relative to branched covers of degree at most n (with Benson Farb). Submitted for publication.
  2. Solvable Points on Intersections of Quadrics, Cubics and Quartics (with Claudio Gómez-Gonzáles). Submitted for publication.
  3. Correctness, Artificial Intelligence, and the Epistemic Value of Proof (with Jim Weatherall). Submitted for publication.
  4. Lie’s Third Theorem for Lie $\infty$-algebras (with Chris Rogers). Submitted for publication.
  5. A higher Kac-Moody extension for two-dimensional gauge groups (with Jens Kaad and Ryszard Nest). Submitted for publication.
  6. Alexander Ostrowski’s”On Dirichlet Series and Algebraic Differential Equations” (with Erik Christian Hansen and Yonathan Stone). English translation of German original.

Publications:

  1. On Simplicial Principal Bundles in Descent Categories. Homotopical Methods in Geometry and Physics (Getzler 60th Birthday Volume), Contemporary Mathematics, AMS, to appear.
  2. Essential Dimension via Prismatic Cohomology (with Benson Farb and Mark Kisin), Duke Mathematical Journal, vol. 173, 2024, no. 15, pp. 3059-3106.
  3. Fractals in Africanist Music (with Claudio Gómez-Gonzáles, Sidhanth Raman, and Siddharth Viswanath), MAA FOCUS, vol. 44, 2024, no. 4, pp. 18-22.
  4. Generalized Versality, Special Points, and Resolvent Degree for the Sporadic Groups (with Claudio Gomez-Gonzales and Alex Sutherland), Journal of Algebra, vol. 647, 2024, pp. 758-793.
  5. Modular functions and resolvent problems, with an appendix by Nate Harman (with Benson Farb and Mark Kisin). Mathematsche Annalen, vol. 386, 2023, pp. 113-150.
  6. Mathematics and Dance: Notes from an Emerging Interaction (with Reggie Wilson), Notices of the AMS, vol. 68, 2021, no. 11, 1926-1929.
  7. The Essential Dimension of Congruence Covers (with Benson Farb and Mark Kisin), Compositio Mathematica, 157(11), 2021, 2407-2432. doi:10.1112/S0010437X21007594.
  8. A Generalized Contou-Carrere Symbol and its Reciprocity Laws in Higher Dimensions (with Oliver Braunling and Michael Groechenig). Transactions of the AMS, Ser. B vol. 8, 2021, 679-753.
  9. Problems in Arithmetic Topology (with Claudio Gomez-Gonzales). Research in the Mathematical Sciences, vol. 8, 2021, article 23, 14 pp.
  10. Tschirnhaus Transformations after Hilbert, L’Enseignement Mathematique, vol. 66, 2020, no. 3, pp. 489-540.
  11. Resolvent degree, Hilbert’s 13th Problem and Geometry (with Benson Farb). L’Enseignement Mathematique, vol. 65, 2019, no. 3/4, pp. 303-376.
  12. Derived \ell-adic zeta functions (with Jonathan Campbell and Inna Zakharevich). Advances in Mathematics, vol. 354, 2019, article 106760, 53 pp.
  13. Hochschild coniveau spectral sequence and the Beilinson residue (with Oliver Braunling). Pacific Journal of Mathematics, vol. 300, no. 2, 2019, pp. 257-329.
  14. Coincidences of homological densities, predicted by arithmetic (with Benson Farb and Melanie Matchett Wood). Advances in Mathematics, vol. 352, 2019, pp. 670-716.
  15. The A_\infty-Structure of the Index Map (with Oliver Braunling and Michael Groechenig). Annals of K-Theory, vol. 3, no. 4, 2018, pp. 581–614.
  16. Etale homological stability and arithmetic statistics (with Benson Farb). Quarterly Journal of Mathematics, vol. 69, no. 3, 2018, pp. 951–974.
  17. On the normally ordered tensor product and duality for Tate objects (with Oliver Braunling, Michael Groechenig and Aron Heleodoro). Theory and Applications of Categories, vol. 33, 2018, no. 13, pp. 296-349.
    1. Corrigendum to “On the normally ordered tensor product and duality for Tate objects” Theory and Applications of Categories, vol. 39, 2023, no. 7, pp 186-188. (removes erroneous paragraph on top of p. 306, and 2.6-2.8; remainder of paper unaffected).
  18. The Index Map in Algebraic K-Theory (with Oliver Braunling and Michael Groechenig). Selecta Mathematica, vol. 24, no. 2, 2018, pp. 1039-1091.
  19. Resolvent degree, Hilbert’s 13th problem and geometry (with Benson Farb). “Topology of Arrangements and Representation Stability”, Oberwolfach Research Reports, no. 2, 2018, pp. 84–87.
  20. Topology and arithmetic of resultants, II: the resultant = 1 hypersurface (with an appendix by C. Cazanave) (with Benson Farb). Algebraic Geometry, vol. 4, no. 3, 2017, pp. 337-352.
  21. Relative Tate Objects and Boundary Maps in the K-Theory of Coherent Sheaves (with Oliver Braunling and Michael Groechenig). Homology, Homotopy and Applications, vol. 19, no. 1, 2017, pp. 341-369.
  22. Modular Operads of Embedded Curves (with Satoshi Kondo and Charles Siegel). Geometry & Topology, vol. 21, no. 2, 2017, pp. 903-922.
  23. Operator Ideals in Tate Objects (with Oliver Braunling and Michael Groechenig). Mathematical Research Letters, vol. 23, no. 6, 2016, pp. 1565-1631.
  24. Coincidences of homological densities, predicted by arithmetic (with Benson Farb and Melanie Matchett Wood). “Topologie”, Oberwolfach Research Reports, vol. 16, no. 3, 2016, pp. 2041-2043.
  25. Geometric and Analytic Structures on the Higher Adeles (with Oliver Braunling and Michael Groechenig). Research in the Mathematical Sciences, Special Collection in Celebration of the Research of Fedor Bogomolov on the Occasion of his 70th Birthday, vol. 3, no. 1, 2016, article 22.
  26. Topology and arithmetic of resultants, I (with Benson Farb). New York Journal of Mathematics, vol. 22, 2016, pp. 801-821
    1. Corrigendum to “Topology and arithmetic of resultants, I”,  New York Journal of Mathematics, vol. 25, 2019, pp. 195-197. (corrects an error in the original proof of Theorem 1.2; arXiv version above includes this correction)
  27. Tate Objects in Exact Categories (with an appendix by J. Stovicek and J. Trlifaj)  (with Oliver Braunling and Michael Groechenig). Moscow Mathematical Journal, vol. 16, no. 3, 2016, pp. 433-504.
  28. Descent for n-Bundles. Advances in Mathematics, vol. 288, 2016, pp. 527-575.

In Preparation:

  1. Lie’s Second Theorem for L_\infty-algebras (with Chris Rogers)
  2. The Resolvent Degree of Arithmetic Groups (with Claudio Gómez-Gonzáles and Sidhanth Raman).
  3. Derived motivic integration (with Oliver Braunling, Michael Groechenig and Inna Zakharevich)