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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 was previously supported by NSF grant DMS-1701924 and a Henry Merritt Wriston Fellowship from Brown University.
Here is my CV.
Here are my profiles on Google Scholar and MathSciNet.
Research
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Moduli spaces of curves: classical and tropical. Draft of an article submitted to the Notices of the AMS.
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On the top-weight rational cohomology of A_g, with M. Brandt, J. Bruce, M. Melo, G. Moreland, C. Wolfe.
Preprint.
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Relative Richardson varieties, with N. Pflueger.
Preprint.
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The S_n-equivariant 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
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Combinatorial relations on skew Schur and skew stable Grothendieck polynomials, with N. Pflueger.
To appear in Algebraic combinatorics.
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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.
To appear in J. Amer. Math. Soc.
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Topology of the tropical moduli spaces M_{2,n}
To appear in Beiträge zur Algebra und Geometrie
Supplementary sage code for Section 6
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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.
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Euler characteristics of Brill-Noether varieties, with N. Pflueger.
To appear in Transactions of the AMS.
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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 Gieseker-Petri theorem and imposed ramification, with B. Osserman and N. Pflueger.
Bulletin of the LMS 51 (6) (2019), 945-960.
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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.
Moduli of curves, Lect. Notes Unione Mat. Ital., vol. 21, Springer, Cham, 2017, pp. 1–26.
Videos of the lectures are available here.
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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.
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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
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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.
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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.
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Fano schemes of determinants and permanents,
with N. Ilten.
Algebra and Number theory 9-3 (2015), 629--679.
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Rotor-routing and spanning trees on planar graphs, with T. Church and J. Grochow.
Int. Math. Res. Not. 11 (2015), 3225-3244.
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Tropical
Teichmüller and Siegel spaces, with M. Melo and F. Viviani.
Algebraic and combinatorial aspects of tropical geometry,
Contemporary Mathematics 589 (2013), 45-85.
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Tropical curves and metric graphs
Ph.D. dissertation, 107 pages, 2012.
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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
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Tropical hyperelliptic
curves
Journal of Algebraic Combinatorics 37 (2013), no. 2, 331-359.
Slides
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Combinatorics of the
tropical Torelli map
Algebra and Number Theory 6 (2012), no. 6, 1133-1169.
Slides    
Pictures of tropical M_g
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Three notions of tropical
rank for symmetric matrices,
with D. Cartwright.
Combinatorica 32 (2012), no. 1, 55-84.
Slides
   
Extended
abstract
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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
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The distinguishing
number of the augmented cube and hypercube powers
Discrete Mathematics 308 (2008) no. 11, 2330-2336.
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Improved pebbling
bounds,
with A. Godbole.
Discrete Mathematics 308 (2008) no. 11,
2301-2306.
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The distinguishing
number of the direct product and wreath product action
Journal of Algebraic Combinatorics 24 (2006), no. 3, 331-345.
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The maximum
distinguishing number of a group
Electronic Journal of Combinatorics 13 (2006), no. 1, R70.
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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
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Math 540, Honors linear algebra, Summer 2021
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Math 2520, Algebra, Spring 2021
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Math 2520, Algebra, Spring 2020
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Math 750, Introduction to higher mathematics: combinatorics, Fall 2019
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Math 2050, Algebraic geometry, Fall 2019
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Math 2520, Algebra, Spring 2019
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Math 760, Introduction to higher mathematics: algebra, Spring 2019
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Math 2050, Algebraic geometry, Fall 2017
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Math 750, Introduction to higher mathematics: combinatorics, Fall 2017
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Math 1530, Abstract algebra, Spring 2017
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Math 1040, Fundamental problems in geometry, Spring 2016
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Math 0540, Honors Linear Algebra, Fall 2015
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Math 137, Algebraic geometry, Spring 2014 (Harvard)
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Math Ma, Introduction to functions and calculus, Fall 2013 (Harvard)
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Math 285y, Tropical geometry, Spring 2013 (Harvard)
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Math 233a, Theory of schemes, Fall 2012 (Harvard)
Travel/Events/Online events
- Cross Atlantic Representation Theory and Other topics ONline
(CARTOON), May 29-31, 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_n-equivariant top-weight 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 27-31, 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 1-5, 2021
Past travel
Students
Miscellaneous
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