Claudia He Yun

About Me

I am a fifth-year graduate student at Brown University under the supervision of Melody Chan. My research interests include tropical geometry and combinatorics. I did my undergraduate studies at Smith College.

Here is my CV.


Contact Me

Email: he_yun at brown dot edu

Office: 012 Kassar House

Research

Published papers and preprints

  1. Homology representations of compactified configurations on graphs applied to M_{2,n},
    with Christin Bibby, Melody Chan, and Nir Gadish.
    Preprint.
    Please check out our Github page for the code and data.

  2. Topology of tropical moduli spaces of weighted stable curves in higher genus,
    with Siddarth Kannan, Shiyue Li, and Stefano Serpente.
    Submitted.

  3. The S_n equivariant homology of the tropical moduli spaces Delta_{2,n}.
    Experimental Mathematics (2021): 1-13.
    Supplementary Sage code.
    Here is     a recording of a talk I gave on this paper at TGiZ.

  4. Puzzling and apuzzling graph,
    with D. Gold, J. Henle, C. Huang, T. Lyve, T. Marin, J.Osorio, M. Puligandla, B. Weick, J. Xia, and J. Zhang. AKCE International Journal of Graphs and Combinatorics, vol. 13, no. 1 (2016): 1-10.

Ongoing projects

  • Tropical degree-two del Pezzo surfaces and their 56 lines,
    with Maria Angelica Cueto, Amanda Knecht, Kalina Mincheva, and Aleksandra Sobieska.
    Degree-two del Pezzo surfaces are blowups of the projective plane at seven generic points. It is a classical result that there are 56 lines on such surfaces. The arrangement of the 56 lines becomes an arrangement of 56 metric trees on the corresponding tropical surfaces and our goal is to describe the possible combinatorics of the tree arrangements as we move along the tropical moduli space of tropical smooth degree-two del Pezzo surfaces, embedded via the Cox ring.

  • Discrete Morse theory for symmetric Delta-complexes.
    We develop a discrete Morse theory for symmetric Delta-complexes.

  • Splines on lattices and the equivariant cohomology of homogenous affine springer fibers of weight 1,
    with Julianna Tymoczko.
    Given some ring R and a graph G whose edges are labelled with ring elements, a generalized algebraic spline on the graph is a labelling of the vertices by elements in R such that the difference between two adjacent vertices lies in the ideal generated by the label of the edge between them. Goresky-Kottwitz-MacPherson proved that for a compact complex manifold with a torus action that satisfies certain hypotheses, we can define an edge-labelled graph, called the moment graph of the manifold, and that the T-equivarient cohomology ring of the manifold is exactly isomorphic to the ring of splines on its moment graph. In this project, we study splines on certain types of infinite graphs.


Teaching

Brown University

Smith College

  • Tutor. All math courses below multivariable calculus and linear algebra, Fall 2016, Spring 2017.

  • Instructor. Introductory Java Programming, Winter 2016.

  • Tutor. CSC 212 Data Structures with Java, Fall 2016.

  • Tutor. PHY 215 Introductory Physics III; PHY 210 Math Methods for Physicists and Engineers, Spring 2015, Fall 2015, Spring 2016.

  • Grader. AST 111 Introductory Astronomy; PHY 117 Introductory Physics I; PHY 215 Introductory Physics III, Fall 2014, Spring 2015.

  • Learning Assistant. PHY 117 Introductory Physics I, Fall 2014.

Others

  • GirlsGetMath @ ICERM . Teaching Assistant. Apportionment. Summer 2019.

  • Summer Science Program. Teaching Assistant and Residential Assistant. Multivariable calculus, Introductory Physics, Introductory Astronomomy, and Python Programming, Summer 2018.


Expository Writings & Slides

  • Stagosaur group E2: Exponential growth of H^{4g-6}(M_g;Q).
    Part I by Brian Hwang. Part II by me. Part III by Shiyue Li.

Outreach

  • I am on the organizing committee of the Brown Math Circle. We organize weekly trips to a local middle school and a local high school to teach math through activities and games.

Travel