Melody Chan

311 Kassar House

Department of Mathematics
Brown University
Box 1917
151 Thayer St
Providence, RI 02912

melody_chan at brown dot edu


Research
Teaching
Miscellaneous

I am a tenure-track assistant professor at Brown University. From 2012 to 2015 I was an NSF Postdoctoral Fellow and Lecturer in the mathematics department at Harvard. I got my PhD from UC Berkeley in 2012, advised by Bernd Sturmfels. I am interested in combinatorial algebraic geometry, particularly: algebraic curves and their moduli, graph theory, and tropical geometry.

I am supported by NSF DMS-1701924 and a 2018 Sloan Research Fellowship, an NSF CAREER grant DMS-1844768 and the 2020 AWM-Microsoft Research Prize. In Spring 2018 I was supported by a Henry Merritt Wriston Fellowship. In Fall 2018 I was on junior sabbatical at ICERM.

Here is my CV. Here are my profiles on Google Scholar and MathSciNet.

Research

  1. The S_n-equivariant top weight Euler characteristic of M_{g,n}, with C. Faber, S. Galatius, and S. Payne.
  2. Topology of moduli spaces of tropical curves with marked points, with S. Galatius and S. Payne.
    This is the second in a series of papers that subsumes the preprint The tropicalization of the moduli space of curves II: Topology and applications.
    Submitted.
  3. Tropical curves, graph complexes, and top weight cohomology of M_g, with S. Galatius and S. Payne.
    This subsumes a part of the preprint The tropicalization of the moduli space of curves II: Topology and applications.
  4. The Gieseker-Petri theorem and imposed ramification, with B. Osserman and N. Pflueger.
    Submitted.
  5. Euler characteristics of Brill-Noether varieties, with N. Pflueger.
    Submitted.
  6. A moduli stack of tropical curves, with R. Cavalieri, M. Ulirsch, and J. Wise.
    Submitted.
  7. Lectures on tropical curves and their moduli spaces
    Notes for a lecture series at the CIMPA-CIMAT-ICTP School on Moduli of Curves, Guanajuato, Mexico.
    Proceedings of the School on Moduli of Curves, Guanajuato, Lecture Notes of the Unione Matematica Italiana, Springer-UMI, to appear.
    Videos of the lectures are available here.
  8. Topology of the tropical moduli spaces M_{2,n}
    Supplementary sage code for Section 6
  9. The expected jaggedness of order ideals, with S. Haddadan, S. Hopkins, L. Moci.
    Forum of Mathematics, Sigma (2017), Vol. 5, e9, 27 pages.
    arxiv version
  10. Genera of Brill-Noether curves and staircase paths in Young tableaux, with A. López Martín, N. Pflueger, M. Teixidor i Bigas.
    Transactions of the AMS, to appear.
  11. Theta characteristics of tropical K_4-curves, with P. Jiradilok.
    Combinatorial Algebraic Geometry (eds. G.G. Smith and B. Sturmfels), to appear.
  12. Sandpiles, spanning trees, and plane duality, with D. Glass, M. Macauley, D. Perkinson, C. Werner, Q. Yang
    SIAM J. Discrete Math 29-1 (2015), 461-471.
  13. Fano schemes of determinants and permanents, with N. Ilten.
    Algebra and Number theory 9-3 (2015), 629--679.
  14. Rotor-routing and spanning trees on planar graphs, with T. Church and J. Grochow.
    Int. Math. Res. Not. 11 (2015), 3225-3244.
  15. Tropical Teichmüller and Siegel spaces, with M. Melo and F. Viviani.
    Algebraic and combinatorial aspects of tropical geometry, Contemporary Mathematics 589 (2013), 45-85.
  16. Tropical curves and metric graphs
    Ph.D. dissertation, 107 pages, 2012.
  17. Elliptic curves in honeycomb form, with B. Sturmfels.
    Algebraic and combinatorial aspects of tropical geometry, Contemporary Mathematics 589 (2013) 87-107.
    Supplementary materials and computations
  18. Tropical hyperelliptic curves
    Journal of Algebraic Combinatorics 37 (2013), no. 2, 331-359.
    Slides
  19. Combinatorics of the tropical Torelli map
    Algebra and Number Theory 6 (2012), no. 6, 1133-1169.
    Slides     Pictures of tropical M_g
  20. Three notions of tropical rank for symmetric matrices, with D. Cartwright.
    Combinatorica 32 (2012), no. 1, 55-84.
    Slides     Extended abstract
  21. The 4x4 minors of a 5xn matrix are a tropical basis, with A. N. Jensen and E. Rubei.
    Linear Algebra and its Applications 435 (2011), no. 7, 1598-1611.
    Slides
  22. The distinguishing number of the augmented cube and hypercube powers
    Discrete Mathematics 308 (2008) no. 11, 2330-2336.
  23. Improved pebbling bounds, with A. Godbole.
    Discrete Mathematics 308 (2008) no. 11, 2301-2306.
  24. The distinguishing number of the direct product and wreath product action
    Journal of Algebraic Combinatorics 24 (2006), no. 3, 331-345.
  25. The maximum distinguishing number of a group
    Electronic Journal of Combinatorics 13 (2006), no. 1, R70.
  26. Stably computable properties of network graphs, with D. Angluin, J. Aspnes, M. J. Fischer, H. Jiang, R. Peralta
    Proceedings of the International Conference on Distributed Computing in Sensor Systems, Lecture Notes in Computer Science, 3560 (2005) 63-74.

Teaching

Travel

Past travel

Students

Miscellaneous