Publications and Preprints

Multitriangulations on the half‑cylinder (2025)                                                       with Saskia Solotko, Katherine Tung, Mengyuan Yang

[arXiv:2506.16598], REU report, slides                                                                                                                                Mentor: Pavlo Pylyavskyy 

We show that for every 𝑛 ≥ 2, the simplicial complex defined by all 2‑triangulations of the 

half‑cylinder with 𝑛 marked points on one boundary component is a weak pseudomanifold. 

We furthermore define chevron pipe dreams that are in bijection with these 2‑triangulations.   

Automorphisms of the fine curve graphs of planar surfaces (2025)                      with Roberta Shapiro, Rohan Wadhwa, Arthur Wang

[arXiv:2506.06142], poster                                                                                                                                                           Mentor: Roberta Shapiro

submitted

We show that the self-homeomorphism group of any planar surface with at least 7 punctures 

is isomorphic to the automorphism group of its fine curve graph.    

Characterizing positroid quotients of uniform matroids (2025)                              with Zhixing Chen, Yumou Fei, Jiyang Gao, Yuxuan Sun

[arXiv:2311.05340], extended abstract                                                                                                                       Mentor: Jiyang Gao

submitted

We prove that every two‑step flag positroid with adjacent ranks can be represented by a cyclic 

shift of decorated permutations, resolving the main conjecture of Benedetti, Chávez, and 

Jiménez (2022). Additionally, we provide combinatorial characterizations for two‑step flag 

positroids where one is a uniform matroid, and for complete flag lattice path matroids.                                                                           

Postnikov–Stanley polynomials are Lorentzian (2024)                                                                           with Serena An, Katherine Tung

[arXiv:2412.02051]                                                                                                                                                                                Mentor: Shiliang Gao  

submitted 

We build a connection between Postnikov–Stanley polynomials and the geometry of

Richardson varieties, and show that Postnikov–Stanley polynomials are Lorentzian.                

Newton polytopes of dual Schubert polynomials (2024)                                                                               with Serena An, Katherine Tung

[arXiv:2411.16654], extended abstract, REU report, poster, slides                                          Mentors: Shiyun Wang, Pavlo Pylyavskyy 

to appear in Algebraic Combinatorics

We characterize the supports of dual Schubert polynomials, and provide two distinct combinatorial

descriptions of the vertices of their Newton polytopes. As a byproduct, we obtain an elementary 

proof of the M‑convexity result established by Huh, Matherne, Mészáros, and St. Dizier (2022).                           

The monoid representation of upho posets and total positivity (2024)                                                        with Ziyao Fu, Yulin Peng

[arXiv:2411.04123], extended abstract, poster                                                                                                   Mentor: Yibo Gao 

We construct a bijection between colored upho posets and certain monoids and show that the                                                               

totally positive functions in 1 + 𝑥ℤ[[𝑥]] are exactly the rank‑generating functions of Schur‑positive 

upho posets, resolving the main conjecture of Gao, Guo, Seetharaman, and Seidel (2022).                                                                                                                     

Conference Papers

Partial flag positroids (2025)                                                                                                       with Zhixing Chen, Yumou Fei, Jiyang Gao, Yuxuan Sun

Séminaire Lotharingien de Combinatoire, 93B (2025), Art. 109 (FPSAC 2025)                                                          Mentor: Jiyang Gao

Newton polytopes of dual Schubert polynomials (2025)                                                                                 with Serena An, Katherine Tung

Séminaire Lotharingien de Combinatoire, 93B (2025), Art. 19 (FPSAC 2025)                                     Mentors: Shiyun Wang, Pavlo Pylyavskyy 

The monoid representation of upho posets and total positivity (2024)                                                          with Ziyao Fu, Yulin Peng

Séminaire Lotharingien de Combinatoire, 91B (2024), Art. 104 (FPSAC 2024)                                                           Mentor: Yibo Gao

Papers in Preparation

Universality of Fomin–Pylyavskyy tilings (2025+)                                                                                             Mentor: Sergey Fomin

Inspired by Hilbert (1902), we show that the master tiling theorem for incidence geometry

established by Fomin and Pylyavskyy (2023) can be used to encode algebraic operations in a field.

As a result, the master theorem could “imply” all incidence theorems in ℂℙ𝑛 but not ℝℙ𝑛.                                                                                                                               

Miscellaneous Writings

•    Total positivity: Total positivity, Schur positivity, and representations of the infinite symmetric group

•    Analytic‑algebraic equivalence: A sketch of Géométrie Algébrique et Géométrie Analytique (after Serre)

•    Local cohomology: Direct summand conjecture in positive characteristic (after Hochster)

•    Lie theory: Lie group–Lie algebra correspondence

Selected Presentations

2025 Partial flag positroids, FPSAC 2025                                                                                                                               Hokkaido, Japan

2025 Dual Schubert polynomials and Postnikov--Stanley polynomials, Michigan Combinatorics Seminar                Ann Arbor, Michigan

2025 Newton polytopes of dual Schubert polynomials, JMM 2025                                                                                  Seattle, Washington

2024 The monoid representation of upho posets and total positivity, FPSAC 2024                                                         Bochum, Germany

2024 The fine curve graph of planar surfaces, LoG(M) poster session 2024                                                                  Ann Arbor, Michigan

    2022 Direct summand conjecture in positive characteristic, Shandong University                                                                    Jinan, China

Research and Work Experience

    2025 Grader for MATH 566 (Algebraic Combinatorics), University of Michigan                                                                          Michigan

    2024 Grader for MATH 668 (Coxeter Groups and Root Systems), University of Michigan                                                          Michigan

2024 Grader for MATH 565 (Combinatorics and Graph Theory), University of Michigan                                                          Michigan

2024 Lab of Geometry at Michigan, mentored by Roberta Shapiro                                                                                                   Michigan

2024 UMN Combinatorics and Algebra REU, mentored by Pavlo Pylyavskyy and Shiyun Wang                                                 Minnesota

2023 PKU Algebra and Combinatorics Experience, PACE, mentored by Yibo Gao and Jiyang Gao                                                   China

2022 Teaching assistant for Advanced Algebra II, Shandong University                                                                                               China