Preprints


  1. Tropical moduli spaces as symmetric Delta-complexes (with D. Allcock and D. Corey)
  2. The Sn-equivariant top weight Euler characteristic of Mg,n (with M. Chan, C. Faber, and S. Galatius)
  3. Compactified Jacobians as Mumford models (with K. Christ and T. Shen)
  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)

In Press


  1. Topology of moduli spaces of tropical curves with marked points (with M. Chan and S. Galatius) To apper in Facets of Algebraic Geometry: Volume in Honour of William Fulton's 80th Birthday

Publications


  1. 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
  2. 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
  3. 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
  4. A tropical motivic Fubini theorem with applications to Donaldson-Thomas theory (with J. Nicaise) Duke Math. J. 168 (2019), no. 10, 1843–1886
  5. Tropical refined curve counting via motivic integration (with J. Nicaise and F. Schroeter) Geom. Topol. 22 (2018), no. 6, 3175–3234
  6. 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
  7. Combinatorial and inductive methods for the tropical maximal rank conjecture (with D. Jensen) J. Combin. Theory Ser. A. 152 (2017), 138–158
  8. Tropical independence II: The maximal rank conjecture for quadrics (with D. Jensen) Algebra Number Theory 10 (2016), no. 8, 1601–1640
  9. 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)
  10. Cremona symmetry in Gromov-Witten theory (with A. Gholampour and D. Karp) Pro Mathematica, 29 (2016), no. 57, 129–149
  11. 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
  12. Topology of nonarchimedean analytic spaces and relations to complex algebraic geometry Bull. Amer. Math. Soc. 52 (2015), no. 2, 223–247
  13. 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
  14. Operational K-theory (with D. Anderson) Doc. Math. 20 (2015), 357–399
  15. Lifting divisors on a generic chain of loops (with D. Cartwright and D. Jensen) Canad. Math. Bull. 58 (2015), no. 2, 250–262
  16. 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
  17. Artificial intelligence for Bidding Hex (with E. Robeva) Games of No Chance 4, MSRI Publications 63 (2015), 207–214
  18. 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
  19. Limits of tropicalizations (with T. Foster and P. Gross) Israel J. Math. 201 (2014), no. 2, 835–846
  20. On the structure of non-archimedean analytic curves (with M. Baker and J. Rabinoff) Contemp. Math. 605 (2013), 93–125
  21. Boundary complexes and weight filtrations Mich. Math. J. 62 (2013), no. 2, 293–322
  22. Lifting tropical intersections (with B. Osserman) Doc. Math. 18 (2013), 121–175
  23. Connectivity of tropicalizations (with D. Cartwright) Math. Res. Lett. 19 (2012), no. 5, 1089–1095
  24. 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
  25. 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
  26. A tropical proof of the Brill-Noether Theorem (with F. Cools, J. Draisma, and E. Robeva) Adv. Math. 230 (2012), no. 2, 759–776
  27. Realization spaces for tropical fans (with E. Katz) Combinatorial aspects of commutative algebra and algebraic geometry, Abel Symp., 6, Springer 2011, 73–88
  28. Discrete bidding games (with M. Develin) Electronic J. Combin. 17 (2010), no. 1, Research Paper 85, 40 pp.
  29. Positivity for toric vector bundles (with M. Hering and M. Mustaţă) Ann. Inst. Fourier 60 (2010), no. 2, 607–640
  30. 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
  31. Analytification is the limit of all tropicalizations Math. Res. Lett. 16 (2009), no. 3, 543–556
  32. Lattice polytopes cut out by root systems and the Koszul property Adv. Math. 220 (2009), no. 3, 926–935
  33. Frobenius splittings of toric varieties Algebra Number Theory 3 (2009), no. 1, 107–119
  34. Correction to Frobenius splittings of toric varieties
  35. Fibers of tropicalization Math. Z. 262 (2009), no. 2, 301–311
  36. Correction to Fibers of tropicalization Math. Z. 272 (2012), no. 3-4, 1403–1406
  37. Toric vector bundles, branched covers of fans, and the resolution property J. Algebraic Geom. 18 (2009), no. 1, 1–36
  38. Bidding chess (with J. Bhatt) Math. Intelligencer 31 (2009), 37–39
  39. Adelic amoebas disjoint from open halfspaces J. Reine Angew. Math. 625 (2008), 115–123
  40. Piecewise polynomials, Minkowski weights, and localization on toric varieties (with E. Katz) Algebra Number Theory 2 (2008), no. 2, 135–155
  41. Moduli of toric vector bundles Compositio Math. 144 (2008), no. 5, 1199–1213
  42. Ehrhart series and lattice triangulations Discr. Comput. Geom. 40 (2008), no. 3, 365–376
  43. Stable base loci, movable curves, and small modifications, for toric varieties Math. Z. 253 (2006), no. 2, 421–431
  44. Equivariant Chow cohomology of toric varieties Math. Res. Lett. 13 (2006), no. 1, 29–41
  45. Asymptotic cohomological functions of toric divisors (with M. Hering and A. Küronya) Adv. Math. 207 (2006), no. 2, 634–645
  46. Fujita’s very ampleness conjecture for singular toric varieties Tohoku Math. J. 58 (2006), no. 3, 447–459
  47. Ehrhart polynomials and stringy Betti numbers (with M. Mustaţă) Math. Ann. 333 (2005), no. 4, 787–795
  48. 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
  49. Alternating graphs (with C. Adams, R. Dorman, K. Foley, and J. Kravis) J. Combin. Theory Ser. B 77 (1999), no. 1, 96–120

Volume Edited


  1. Nonarchimedean and Tropical Geometry (with M. Baker) Simons Symposia, Springer 2016