Melody Chan

311 Kassar House

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

mtchan at math dot 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.

Here is my CV.

Here are my profiles on Google Scholar and MathSciNet.

Research

  1. Tropicalization of the moduli space of curves II: topology and applications, with S. Galatius and S. Payne.
  2. Topology of the tropical moduli spaces M_{2,n}
    Supplementary sage code for Section 6
  3. The expected jaggedness of order ideals, with S. Haddadan, S. Hopkins, L. Moci.
    Submitted.
  4. Genera of Brill-Noether curves and staircase paths in Young tableaux, with A. López Martín, N. Pflueger, M. Teixidor i Bigas.
    Submitted.
  5. Theta characteristics of tropical K_4-curves, with P. Jiradilok.
    Submitted.
  6. 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.
  7. Fano schemes of determinants and permanents, with N. Ilten.
    Algebra and Number theory 9-3 (2015), 629--679.
  8. Rotor-routing and spanning trees on planar graphs, with T. Church and J. Grochow.
    Int. Math. Res. Not. 11 (2015), 3225-3244.
  9. Tropical Teichmüller and Siegel spaces, with M. Melo and F. Viviani.
    Algebraic and combinatorial aspects of tropical geometry, Contemporary Mathematics 589 (2013), 45-85.
  10. Tropical curves and metric graphs
    Ph.D. dissertation, 107 pages, 2012.
  11. 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
  12. Tropical hyperelliptic curves
    Journal of Algebraic Combinatorics 37 (2013), no. 2, 331-359.
    Slides
  13. Combinatorics of the tropical Torelli map
    Algebra and Number Theory 6 (2012), no. 6, 1133-1169.
    Slides     Pictures of tropical M_g
  14. Three notions of tropical rank for symmetric matrices, with D. Cartwright.
    Combinatorica 32 (2012), no. 1, 55-84.
    Slides     Extended abstract
  15. 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
  16. The distinguishing number of the augmented cube and hypercube powers
    Discrete Mathematics 308 (2008) no. 11, 2330-2336.
  17. Improved pebbling bounds, with A. Godbole.
    Discrete Mathematics 308 (2008) no. 11, 2301-2306.
  18. The distinguishing number of the direct product and wreath product action
    Journal of Algebraic Combinatorics 24 (2006), no. 3, 331-345.
  19. The maximum distinguishing number of a group
    Electronic Journal of Combinatorics 13 (2006), no. 1, R70.
  20. 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

Stuff I organize