Preprints


  1. Hopf structures in the cohomology of Ag, GLn(Z), and SLn(Z) (with F. Brown, M. Chan, and S. Galatius)
  2. Moduli spaces of curves with polynomial point counts (with S. Canning, H. Larson, and T. Willwacher)
  3. The motivic structures LS12 and S16 in the cohomology of moduli spaces of curves (with S. Canning, H. Larson, and T. Willwacher)
  4. The Kodaira dimensions of M22 and M23 (with G. Farkas and D. Jensen)
  5. Adic tropicalizations and cofinality of Gubler models (with T. Foster)
  6. The local motivic monodromy conjecture for simplicial nondegenerate singularities (with M. Larson and A. Stapledon)

In Press


  1. Recent developments in Brill–Noether theory (with D. Jensen) To appear in EMS Volume for the BMS Thematic Einstein Semester on Algebraic Geometry
  2. Weight two compactly supported cohomology of moduli spaces of curves (with T. Willwacher) To appear in Duke Math. J.
  3. The weight two compactly supported Euler characteristic of moduli spaces of curves (with T. Willwacher) To appear in Pure Appl. Math. Q. volume in honor of Enrico Arbarello

Publications


  1. Polynomial point counts and odd cohomology vanishing on moduli spaces of stable curves (with J. Bergström and C. Faber) Ann. Math. (2) 199 (2024), no. 3, 1323–1365
  2. Extensions of tautological rings and motivic structures in the cohomology of Mg,n (with S. Canning and H. Larson) Forum Math. Pi 12 (2024) Paper No. e23, 31 pp.
  3. The non-abelian Brill-Noether divisor on M13 and the Kodaira dimension of R13 (with G. Farkas and D. Jensen) Geom. Topol. 28 (2024), no. 2, 803–866
  4. K-theory of wonderful varieties and matroids (with M. Larson, S. Li, and N. Proudfoot)
    5. Adv. Math. 441 (2024), Paper No. 109554, 43 pp.
  5. Avoidance loci and real bitangents to plane quartics (with H. Markwig and K. Shaw) Proc. Roy. Soc. Edinburgh Sect. A 154 (2024), no. 4, 1308–1312
  6. Weight 11 compactly supported cohomology of moduli spaces of curves (with T. Willwacher). Int. Math. Res. Not. IMRN (2024), no. 8, 7060–7098
  7. The Sn-equivariant top weight Euler characteristic of Mg,n (with M. Chan, C. Faber, and S. Galatius). Amer. J. Math. 145 (2023), no. 5, 1549–1585
  8. The eleventh cohomology group of Mg,n (with S. Canning and H. Larson) Forum Math. Sigma 11 (2023), Paper No. e62, 18 pages
  9. Resolutions of local face modules, functoriality, and vanishing of local h-vectors (with M. Larson and A. Stapledon) Algebr. Comb. 6 (2023), no. 4, 1057–1072
  10. Bitangents to plane quartics via tropical geometry: rationality, A1-enumeration, and real signed count (with H. Markwig and K. Shaw) Res. Math. Sci. 10 (2023), no. 2, Paper No. 21, 54 pages
  11. Compactified Jacobians as Mumford models (with K. Christ and T. Shen) Trans. Amer. Math. Soc. 376 (2023), no. 7, 4605–4630
  12. Tropical moduli spaces as symmetric Delta-complexes (with D. Allcock and D. Corey) Bull. Lond. Math. Soc. 54 (2022), no. 1, 193–205
  13. Topology of moduli spaces of tropical curves with marked points (with M. Chan and S. Galatius) Facets of Algebraic Geometry. Vol. I. A Collection in Honor of William Fulton’s 80th Birthday, 77-131. London Mathematical Society Lecture Note Series, Vol. 472, Cambridge University Press, 2022
  14. Tropical curves, graph complexes, and top weight cohomology of Mg (with M. Chan and S. Galatius) J. Amer. Math. Soc. 34 (2021), no. 2, 565–594
  15. Equivariant Grothendieck-Riemann-Roch and localization in operational K-theory (with D. Anderson and R. Gonzales, with an appendix by G. Vezzosi) Algebra Number Theory 15 (2021), no. 2, 341–385
  16. Triangulations of simplices with vanishing local h-polynomial (with E. Gunther, A. Moura, A. Stapledon, and J. Schuchardt) Algebr. Comb. 3 (2020), no. 6, 1417–1430
  17. A tropical motivic Fubini theorem with applications to Donaldson-Thomas theory (with J. Nicaise) Duke Math. J. 168 (2019), no. 10, 1843–1886
  18. Tropical refined curve counting via motivic integration (with J. Nicaise and F. Schroeter) Geom. Topol. 22 (2018), no. 6, 3175–3234
  19. Diagonal splittings of toric varieties and unimodularity (with J. Chou, M. Hering, R. Tramel, and B. Whitney) Proc. Amer. Math. Soc. 146 (2018), no. 5, 1911–1920
  20. Combinatorial and inductive methods for the tropical maximal rank conjecture (with D. Jensen) J. Combin. Theory Ser. A. 152 (2017), 138–158
  21. Tropical independence II: The maximal rank conjecture for quadrics (with D. Jensen) Algebra Number Theory 10 (2016), no. 8, 1601–1640
  22. Nonarchimedean geometry, tropicalization, and metrics on curves (with M. Baker and J. Rabinoff) Algebraic Geometry 3 (2016), no. 1, 63–105 (See also arXiv:1104.0320v2)
  23. Cremona symmetry in Gromov-Witten theory (with A. Gholampour and D. Karp) Pro Mathematica, 29 (2016), no. 57, 129–149
  24. The tropicalization of the moduli space of curves (with D. Abramovich and L. Caporaso) Ann. Sci. Éc. Norm. Supér. 48 (2015), no. 4, 765–809
  25. Topology of nonarchimedean analytic spaces and relations to complex algebraic geometry Bull. Amer. Math. Soc. 52 (2015), no. 2, 223–247
  26. On a Cohen-Lenstra heuristic for Jacobians of random graphs (with J. Clancy, N. Kaplan, T. Leake, and M. Wood) J. Algebraic Combin. 42 (2015), no. 3, 701–723
  27. Operational K-theory (with D. Anderson) Doc. Math. 20 (2015), 357–399
  28. Lifting divisors on a generic chain of loops (with D. Cartwright and D. Jensen) Canad. Math. Bull. 58 (2015), no. 2, 250–262
  29. A note on Tutte polynomials, Jacobians, and two variable zeta functions of graphs (with J. Clancy and T. Leake) Exp. Math. 24 (2015), no. 1, 1–7
  30. Artificial intelligence for Bidding Hex (with E. Robeva) Games of No Chance 4, MSRI Publications 63 (2015), 207–214
  31. Tropical independence I: Shapes of divisors and a proof of the Gieseker-Petri Theorem (with D. Jensen) Algebra Number Theory 8 (2014), no. 9, 2043–2066
  32. Limits of tropicalizations (with T. Foster and P. Gross) Israel J. Math. 201 (2014), no. 2, 835–846
  33. On the structure of non-archimedean analytic curves (with M. Baker and J. Rabinoff) Contemp. Math. 605 (2013), 93–125
  34. Boundary complexes and weight filtrations Mich. Math. J. 62 (2013), no. 2, 293–322
  35. Lifting tropical intersections (with B. Osserman) Doc. Math. 18 (2013), 121–175
  36. Connectivity of tropicalizations (with D. Cartwright) Math. Res. Lett. 19 (2012), no. 5, 1089–1095
  37. A note Brill-Noether theory and rank determining sets for metric graphs (with C. M. Lim and N. Potashnik) Int. Math. Res. Not. IMRN (2012), no. 23, 5484–5504
  38. Cox rings and pseudoeffective cones of projectivized toric vector bundles (with J. González, M. Hering, and H. Süβ) Algebra Number Theory 6 (2012), no. 5, 995–1017
  39. A tropical proof of the Brill-Noether Theorem (with F. Cools, J. Draisma, and E. Robeva) Adv. Math. 230 (2012), no. 2, 759–776
  40. Realization spaces for tropical fans (with E. Katz) Combinatorial aspects of commutative algebra and algebraic geometry, Abel Symp., 6, Springer 2011, 73–88
  41. Discrete bidding games (with M. Develin) Electronic J. Combin. 17 (2010), no. 1, Research Paper 85, 40 pp.
  42. Positivity for toric vector bundles (with M. Hering and M. Mustaţă) Ann. Inst. Fourier 60 (2010), no. 2, 607–640
  43. Cayley decompositions of lattice polytopes and upper bounds for h∗-polynomials (with C. Haase and B. Nill) J. Reine Angew. Math. 637 (2009), 207–216
  44. Analytification is the limit of all tropicalizations Math. Res. Lett. 16 (2009), no. 3, 543–556
  45. Lattice polytopes cut out by root systems and the Koszul property Adv. Math. 220 (2009), no. 3, 926–935
  46. Frobenius splittings of toric varieties Algebra Number Theory 3 (2009), no. 1, 107–119
    47. Correction to Frobenius splittings of toric varieties
  47. Fibers of tropicalization Math. Z. 262 (2009), no. 2, 301–311
    48. Correction to Fibers of tropicalization Math. Z. 272 (2012), no. 3-4, 1403–1406
  48. Toric vector bundles, branched covers of fans, and the resolution property J. Algebraic Geom. 18 (2009), no. 1, 1–36
  49. Bidding chess (with J. Bhatt) Math. Intelligencer 31 (2009), 37–39
  50. Adelic amoebas disjoint from open halfspaces J. Reine Angew. Math. 625 (2008), 115–123
  51. Piecewise polynomials, Minkowski weights, and localization on toric varieties (with E. Katz) Algebra Number Theory 2 (2008), no. 2, 135–155
  52. Moduli of toric vector bundles Compositio Math. 144 (2008), no. 5, 1199–1213
  53. Ehrhart series and lattice triangulations Discr. Comput. Geom. 40 (2008), no. 3, 365–376
  54. Stable base loci, movable curves, and small modifications, for toric varieties Math. Z. 253 (2006), no. 2, 421–431
  55. Equivariant Chow cohomology of toric varieties Math. Res. Lett. 13 (2006), no. 1, 29–41
  56. Asymptotic cohomological functions of toric divisors (with M. Hering and A. Küronya) Adv. Math. 207 (2006), no. 2, 634–645
  57. Fujita’s very ampleness conjecture for singular toric varieties Tohoku Math. J. 58 (2006), no. 3, 447–459
  58. Ehrhart polynomials and stringy Betti numbers (with M. Mustaţă) Math. Ann. 333 (2005), no. 4, 787–795
  59. Smooth complete toric threefolds with no nontrivial nef line bundles (with O. Fujino) Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 10, 174–179
  60. Alternating graphs (with C. Adams, R. Dorman, K. Foley, and J. Kravis) J. Combin. Theory Ser. B 77 (1999), no. 1, 96–120

Volumes Edited


  1. Facets of Algebraic Geometry. Vols. I–II. A Collection in Honor of William Fulton’s 80th Birthday. (with P. Aluffi, D. Anderson, M. Hering, and M. Mustaţă) London Mathematical Society Lecture Note Series, Vols. 472–473. Cambridge University Press, 2022
  2. Nonarchimedean and Tropical Geometry (with M. Baker) Simons Symposia, Springer 2016