
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 DMS1844768, and the 2020 AWMMicrosoft 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 DMS1701924 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

On the weight zero compactly supported cohomology of H_{g,n}, with M. Brandt and S. Kannan.

A Serre spectral sequence for the moduli space of tropical curves, with C. Bibby, N. Gadish, and C. Yun.

Homology representations of compactified configurations on graphs applied to M_{2,n}, with C. Bibby, N. Gadish, and C. Yun.
Exp. Math, to appear.

On the topweight rational cohomology of A_g, with M. Brandt, J. Bruce, M. Melo, G. Moreland, C. Wolfe.
Geometry and Topology, to appear.

Relative Richardson varieties, with N. Pflueger.
Math. Proc. Cambridge Philos. Soc., to appear.

The S_nequivariant 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

Moduli spaces of curves: classical and tropical. Notices Amer. Math. Soc. 68 (2021), no. 10, 1700–1713.

Combinatorial relations on skew Schur and skew stable Grothendieck polynomials, with N. Pflueger.
Algebraic combinatorics 4 (1) (2021), 175188.

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), 565594.

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

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.

Euler characteristics of BrillNoether varieties, with N. Pflueger.
Transactions of the AMS, 374 (2021), 15131533.

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
The GiesekerPetri theorem and imposed ramification, with B. Osserman and N. Pflueger.
Bulletin of the LMS 51 (6) (2019), 945960.

Lectures on tropical curves and their moduli spaces
Moduli of curves, Lect. Notes Unione Mat. Ital., vol. 21, Springer, Cham, 2017, pp. 1–26.

Genera of BrillNoether 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.

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

Theta characteristics of tropical K_4curves,
with P. Jiradilok.
Combinatorial Algebraic Geometry Fields Inst. Commun., vol. 80, Fields Inst. Res. Math. Sci., Toronto, ON, 2017, pp. 65–86.

Sandpiles, spanning trees, and plane duality,
with D. Glass, M. Macauley, D. Perkinson, C. Werner, Q. Yang
SIAM J. Discrete Math 291 (2015), 461471.

Fano schemes of determinants and permanents,
with N. Ilten.
Algebra and Number theory 93 (2015), 629679.

Rotorrouting and spanning trees on planar graphs, with T. Church and J. Grochow.
Int. Math. Res. Not. 11 (2015), 32253244.

Tropical
Teichmüller and Siegel spaces, with M. Melo and F. Viviani.
Algebraic and combinatorial aspects of tropical geometry,
Contemporary Mathematics 589 (2013), 4585.

Tropical curves and metric graphs
Ph.D. dissertation, 107 pages, 2012.

Elliptic curves in
honeycomb form,
with B. Sturmfels.
Algebraic and combinatorial aspects of tropical geometry,
Contemporary Mathematics 589 (2013) 87107.
Supplementary materials and
computations

Tropical hyperelliptic
curves
Journal of Algebraic Combinatorics 37 (2013), no. 2, 331359.
Slides

Combinatorics of the
tropical Torelli map
Algebra and Number Theory 6 (2012), no. 6, 11331169.
Slides
Pictures of tropical M_g

Three notions of tropical
rank for symmetric matrices,
with D. Cartwright.
Combinatorica 32 (2012), no. 1, 5584.
Slides
Extended
abstract

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, 15981611.
Slides

The distinguishing
number of the augmented cube and hypercube powers
Discrete Mathematics 308 (2008) no. 11, 23302336.

Improved pebbling
bounds,
with A. Godbole.
Discrete Mathematics 308 (2008) no. 11,
23012306.

The distinguishing
number of the direct product and wreath product action
Journal of Algebraic Combinatorics 24 (2006), no. 3, 331345.

The maximum
distinguishing number of a group
Electronic Journal of Combinatorics 13 (2006), no. 1, R70.

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) 6374.
Expository notes, videos
Course Notes
Expository articles and surveys
Some videos of lectures
 The topweight cohomology of A_g, at BIRS Cohomology of Arithmetic Groups: Duality, Stability, and Computations, October 2021
 Tropical moduli spaces and the cohomology of M_{g,n}, at MSRI Recent Progress in Moduli Theory, May 2019
 Lectures on tropical curves and their moduli spaces. Five lectures at the CIMPACIMATICTP School on Moduli of Curves, Guanajuato, Mexico, 2016 (notes)
Conferences/events/online events
 ICERM Reunion event: Combinatorial Algebraic Geometry, July 31August 18, 2023
 FPSAC 2023, UC Davis, July 1721, 2023
 AGNES summer school: Intersection theory on moduli spaces, July 1114, 2023
 Arithmetic, Birational Geometry,
and Moduli Spaces, Brown University, June 12June 16, 2023
 Stanford algebraic geometry seminar, June 2, 2023
 Oberwolfach Tropical methods in Geometry, May 1519, 2023
 Minnesota topology seminar, May 1, 2023
 Princeton University Horizons Lectures, April 2627, 2023
 Yale colloquium, April 5, 2023
 Louisiana State colloquium and AWM student talk, March 3031, 2023
 Harvard algebraic geometry seminar, March 28, 2023
 Georgia Tech colloquium, March 9, 2023
Past travel
Graduate students, current and former
Teaching

Math 2710O, Topics in Combinatorics, Fall 2022
 Math 2720T, Graphs, matroids, and moduli spaces, Spring 2022

Math 540, Honors linear algebra, Summer 2021

Math 2520, Algebra, Spring 2021

Math 2520, Algebra, Spring 2020

Math 750, Introduction to higher mathematics: combinatorics, Fall 2019

Math 2050, Algebraic geometry, Fall 2019

Math 2520, Algebra, Spring 2019

Math 760, Introduction to higher mathematics: algebra, Spring 2019

Math 2050, Algebraic geometry, Fall 2017

Math 750, Introduction to higher mathematics: combinatorics, Fall 2017

Math 1530, Abstract algebra, Spring 2017

Math 1040, Fundamental problems in geometry, Spring 2016

Math 0540, Honors Linear Algebra, Fall 2015

Math 137, Algebraic geometry, Spring 2014 (Harvard)

Math Ma, Introduction to functions and calculus, Fall 2013 (Harvard)

Math 285y, Tropical geometry, Spring 2013 (Harvard)

Math 233a, Theory of schemes, Fall 2012 (Harvard)
Miscellaneous
