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 an Associate Professor of Mathematics 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 a 2018 Sloan Research Fellowship, an NSF CAREER grant DMS-1844768, and the 2020 AWM-Microsoft Research Prize. I am also currently supported by an NSF FRG (Focused Research Group) award with June Huh, Nick Proudfoot, and Sam Payne. I was previously supported by NSF grant DMS-1701924 and a Henry Merritt Wriston Fellowship from Brown University.

I am a 2022 Fellow of the American Mathematical Society. In 2023, I am on sabbatical, supported by a Simons Foundation Fellowship.

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

Research

  1. Hopf algebras in the cohomology of A_g, GL_n(Z), and SL_n(Z), with F. Brown, S. Galatius, and S. Payne.
  2. On the weight zero compactly supported cohomology of H_{g,n}, with M. Brandt and S. Kannan. Forum of Mathematics, Sigma.
  3. A Serre spectral sequence for the moduli space of tropical curves, with C. Bibby, N. Gadish, and C. Yun.
  4. Homology representations of compactified configurations on graphs applied to M_{2,n}, with C. Bibby, N. Gadish, and C. Yun.
    Exp. Math, to appear.
  5. On the top-weight rational cohomology of A_g, with M. Brandt, J. Bruce, M. Melo, G. Moreland, C. Wolfe.
    Geometry and Topology, to appear.
  6. Relative Richardson varieties, with N. Pflueger.
    Math. Proc. Cambridge Philos. Soc., to appear.
  7. The S_n-equivariant top weight Euler characteristic of M_{g,n}, with C. Faber, S. Galatius, and S. Payne.
    Amer. J. Math., to appear.
    Notes and exercises for a lecture series on this work
  8. Moduli spaces of curves: classical and tropical. Notices Amer. Math. Soc. 68 (2021), no. 10, 1700–1713.
  9. Combinatorial relations on skew Schur and skew stable Grothendieck polynomials, with N. Pflueger.
    Algebraic combinatorics 4 (1) (2021), 175-188.
  10. 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.
    J. Amer. Math. Soc. 34 (2) (2021), 565-594.
  11. Topology of the tropical moduli spaces M_{2,n}
    Beiträge zur Algebra und Geometrie 63 (2022), no. 1, 69–93.
    Supplementary sage code for Section 6
  12. 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.
    Facets of algebraic geometry. Vol. I, 77–131, London Math. Soc. Lecture Note Ser., 472, Cambridge Univ. Press, Cambridge, 2022.
  13. Euler characteristics of Brill-Noether varieties, with N. Pflueger.
    Transactions of the AMS, 374 (2021), 1513-1533.
  14. A moduli stack of tropical curves, with R. Cavalieri, M. Ulirsch, and J. Wise.
    Forum of Mathematics Sigma, 8, E23 (2020). doi:10.1017/fms.2020.16
    15. The Gieseker-Petri theorem and imposed ramification, with B. Osserman and N. Pflueger.
    Bulletin of the LMS 51 (6) (2019), 945-960.
  15. Lectures on tropical curves and their moduli spaces
    Moduli of curves, Lect. Notes Unione Mat. Ital., vol. 21, Springer, Cham, 2017, pp. 1–26.
  16. 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 370 (2018), no. 5, 3405–3439.
  17. 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
  18. Theta characteristics of tropical K_4-curves, with P. Jiradilok.
    Combinatorial Algebraic Geometry Fields Inst. Commun., vol. 80, Fields Inst. Res. Math. Sci., Toronto, ON, 2017, pp. 65–86.
  19. 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.
  20. Fano schemes of determinants and permanents, with N. Ilten.
    Algebra and Number theory 9-3 (2015), 629--679.
  21. Rotor-routing and spanning trees on planar graphs, with T. Church and J. Grochow.
    Int. Math. Res. Not. 11 (2015), 3225-3244.
  22. Tropical Teichmüller and Siegel spaces, with M. Melo and F. Viviani.
    Algebraic and combinatorial aspects of tropical geometry, Contemporary Mathematics 589 (2013), 45-85.
  23. Tropical curves and metric graphs
    Ph.D. dissertation, 107 pages, 2012.
  24. 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
  25. Tropical hyperelliptic curves
    Journal of Algebraic Combinatorics 37 (2013), no. 2, 331-359.
    Slides
  26. Combinatorics of the tropical Torelli map
    Algebra and Number Theory 6 (2012), no. 6, 1133-1169.
    Slides     Pictures of tropical M_g
  27. Three notions of tropical rank for symmetric matrices, with D. Cartwright.
    Combinatorica 32 (2012), no. 1, 55-84.
    Slides     Extended abstract
  28. 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
  29. The distinguishing number of the augmented cube and hypercube powers
    Discrete Mathematics 308 (2008) no. 11, 2330-2336.
  30. Improved pebbling bounds, with A. Godbole.
    Discrete Mathematics 308 (2008) no. 11, 2301-2306.
  31. The distinguishing number of the direct product and wreath product action
    Journal of Algebraic Combinatorics 24 (2006), no. 3, 331-345.
  32. The maximum distinguishing number of a group
    Electronic Journal of Combinatorics 13 (2006), no. 1, R70.
  33. 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.

Expository notes, videos

Course Notes

Expository articles and surveys

Some videos of lectures

Conferences/events/online events

Past travel

Graduate students

Current graduate students

Past graduate students

Teaching

Miscellaneous