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

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

On the topweight rational cohomology of A_g, with M. Brandt, J. Bruce, M. Melo, G. Moreland, C. Wolfe.
Submitted.

Relative Richardson varieties, with N. Pflueger.
Preprint.

The S_nequivariant top weight Euler characteristic of M_{g,n}, with C. Faber, S. Galatius, and S. Payne.
Submitted.
Notes and exercises for a lecture series on this work

Moduli spaces of curves: classical and tropical. To appear in the the Notices of the AMS, November 2021.

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 (2021), 125.
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.
To appear in the Fulton 80 volume.

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
Notes for a lecture series at the CIMPACIMATICTP School on Moduli of Curves, Guanajuato, Mexico.
Moduli of curves, Lect. Notes Unione Mat. Ital., vol. 21, Springer, Cham, 2017, pp. 1–26.
Videos of the lectures are available here.

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.
Teaching

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)
Travel/Events/Online events
 FPSAC 2023, UC Davis
 AMS Fall Eastern Sectional Meeting plenary talk and AMS special session, Amherst, October 12, 2022
 Spec Qbar, Fields Institute, Toronto, July 68, 2022
 Combinatorial, Computational, and Applied Algebraic Geometry, June 27July 1, 2022
 Gustafsson SymposiumInstitut MittagLeffler, Stockholm, May 30June 1, 2022
 Moduli of curves in Stockholm, Carel Faber birthday conference, June 23, 2022
 COGENT online seminar, April 4, 2022
 Graph Complexes and Quantum Field Theory, Berlin, March 28April 1, 2022
 Columbia algebraic geometry seminar, October 22, 2021
 Workshop Series on NonArchimedean and Tropical Geometry, October 15, 2021
 BIRS Cohomology of Arithmetic Groups: Duality, Stability, and Computations, October 1015, 2021
 Mathematics Colloquium, McMaster University, October 8, 2021
 EWM/EMS MittagLeffler Summer School on Tropical Moduli Spaces, June 28July 2, 2021
 Mathematics Colloquium, University of Warwick, June 4, 2021.
 UC Davis Algebraic geometry seminar, May 4, 2021.
 BrandeisHarvardMITNortheastern Joint Mathematics Colloquium, April 15, 2021.
 Algebra, Geometry, and Combinatorics online seminar, September 22, 2020.
 Cross Atlantic Representation Theory and Other topics ONline
(CARTOON), May 2931, 2020. I had the honor of moderating the panel How individuals are dealing with the pandemic.
 Colloquium for EDGE: Enhancing Diversity in Graduate Education: Counting in the presence of symmetry, June 11, 2020.
 Algebraic and tropical online meetings (ATOM), The S_nequivariant topweight Euler characteristic of M_{g,n}, Summer 2020.
Lecture notes, exercises, and hints/solutions for the lecture series.
Videos of the lecture series.
 Women in Algebraic Geometry, ICERM, Providence, RI, July 2731, 2020, virtual.
 Algebra, geometry, combinatorics online, September 22, 2020.
 BATMOBILE, November 9, 2020. Poster
 Semester program in Combinatorial Algebraic Geometry, ICERM, Providence, RI, Spring 2021
 Introductory Workshop: Combinatorial Algebraic Geometry ICERM, Providence, RI, February 15, 2021
Past travel
Students
Miscellaneous
