Research interset Cluster algebras, Mirror symmetry for cluster varieties, and the relation between representation theory and mirror symmetry.
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  • Some Examples of Family Floer Mirror (joint with Yu-shen Lin)
  • Grassmannian categories of infinite rank (joint with Jenny August, Eleonore Faber, Sira Gratz, Sibylle Schroll)
  • Quantization of deformed cluster Poisson varieties (joint with Juan Bosco Fr\'ias-Medina and Timothy Magee)
  • Compactifications of cluster varieties and convexity (joint with Timothy Magee, Alfredo Najera-Chavez)
  • Theta functions and quiver Grassmannians
  • Donaldson-Thomas invariants from tropical disks (joint with Travis Mandel), Selecta Math. (N.S.), vol. ~26, no. 57, 2020
  • Tropical techniques in cluster theory and enumerative geometry, PhD thesis
  • The greedy basis equals the theta basis (joint with Mark Gross, Greg Muller, Gregg Musiker, Dylan Rupel, Salvature Stella, Harold Williams), Journal of Combinatorial Theory, Series A, 145, 150-171
  • Faithful Realizability of Tropical Curves (joint with Lorenzo Fantini, Jennifer Park, Martin Ulirsch), International Mathematics Research Notices , 2016(15), 4706-4727
  • Symmetrizing Tableaux and the 5th case of the Foulkes Conjecture (joint with Christian Ikenmeyer, Sevak Mrchtkyan) Journal of Symbolic Computation , 80, 833-843
  • Ricci flow and curvature on the variety of flags on the two dimensional projective space over the complexes, quaternions and the octonions, (joint with Nolan Wallach) Proc. Amer. Math. Soc. 143 (2015), 369-378
  • The model orbit in G_2, Master thesis (under supervision of Jing-Song Huang)
Conference proceedings:
  • Algebraic and symplectic viewpoint on compactifications of two-dimensional cluster varieties of finite type (joint with Renato Viann), to appear 2019 MATRIX Annuals
  • An example of family Floer mirror, Oberwolfach Mini-Workshop: Superpotentials in Algebra and Geometry
In preparation:
  • Grassmannian cluster categories of type A∞ (joint with Jenny August, Eleonore Faber, Sira Gratz, Sibylle Schroll)
  • On clusterduality for Grassmannians (joint with Lara Bossinger, Timothy Magee, Alfredo Najera-Chavez)
  • Theta basis for generalized cluster algebras (joint with Elizabeth Kelley, Gregg Musiker)