Volume Edited


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

Preprints


  1. A tropical motivic Fubini theorem with applications to Donaldson-Thomas theory. (with J. Nicaise). Submitted.
  2. The tropicalization of the moduli space of curves II. (with M. Chan and S. Galatius). Submitted.
  3. Tropical refined curve counting via motivic integration. (with J. Nicaise and F. Schroeter). Submitted.
  4. Diagonal splittings of toric varieties and unimodularity. (with J. Chou, M. Hering, R. Tramel, and B. Whitney. To appear in Proc. Amer. Math. Soc.

Publications


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