Yibo Gao - REU

PACE (PKU Algebraic Combinatorics Experience) is an eight-week summer REU (Research Experience for Undergraduates) that I started in 2023, thanks to the great support of the Beijing International Center for Mathematical Research and Peking University. Our structure resembles UMN Combinatorics and Algebra REU.

Each student group is required to deliver a final report. Links to manuscripts are provided for projects close to publication. All other reports are available upon requests.

PACE 2028

PACE will be skipped due to FPSAC 2028.

PACE 2026

The top degree and an Orlik-Solomon bound for Solomon-Terao algebras. Hanyu Cai, Haiyang Chen, Shixuan Zeng, Shanwei Zhang. Mentor: Yibo Gao, Tao Gui.
Kazhdan-Lusztig polynomials of value 3 and irreducible singular loci. Zhitong Alex Li, Shixuan Zeng, Xinyuan Zhang. Mentor: Gaston Burrull.
Change of parameters in Hall-Littlewood functions. Ziyi Dai, Qilin Hou, Edward Tong. Mentor: Aritra Bhattacharya.
Permutation representations on cohomology of toric varieties. TChushi Qin, Kaizhe Shen. Mentor: Tao Gui.
Incidence geometry with polarity and tiled surfaces. Peixuan Liu, Zhiyuan Liu, Yuanqi Jiang. Mentor: Yuchong Zhang.
Counting lattice points in Minkowski sums of cross polytopes. Ziyi Dai, Qilin Hou, Zhiyuan Liu, Hongyu Wang. Mentor: Warut Thawinrak.
Double set-valued tableaux and K-theory of the Grassmannian. Yuanqi Jiang, Xiaomeng Zhao. Mentor: Yulin Peng, Sylvester W. Zhang.
On the topology of combinatorial flag varieties. Haiyang Chen, Gekuan Li, Peixuan Liu, Edward Tong, Xiaomeng Zhao. Mentor: Jidong Wang.

PACE 2025

RO(Q8)-Graded Homotopy Groups of Height 2 Lubin-Tate Theory. Jinri Liang, Tianyi Lu, Fenglin Yu, Zhexi Zhang. Mentor: Guchuan Li.
Random permutations from Both-Samelson varieties. Jingqi Li, Haorun Yin, Wenbin Yu. Mentor: Shiliang Gao.
Realizations and Uniqueness of Cut Complexes of Graphs. Yufeng Shen, Zhiyu Song, Feneglin Yu, Leopold Wuhan Zhou, Jingqi Zhuang. Mentor: Lei Xue.
Neighborhood Complexes of induced k-independent graphs. Yufeng Shen, Zhiyu Song, Feneglin Yu, Leopold Wuhan Zhou, Jingqi Zhuang. Mentor: Lei Xue.
Homotopy Type of Total Cut Complexes of Squared Cycle Graphs. Yufeng Shen, Zhiyu Song, Feneglin Yu, Leopold Wuhan Zhou, Jingqi Zhuang. Mentor: Lei Xue.
Enumeration of finite distance monoids. Yunjie Luo, Jie Sheng. Mentor: Kyle Gannon.
Mixed subdivisions and generalized tropical oriented matroids. Tianyu Jiang, Qingyue Yu, Chenyi Zhang. Mentor: Yannick Yao.
Alternating sign matrix and its algebra. Tianyi Lu, Zhouyi Wu, Haorun Yin, Wenbin Yu. Mentor: Sylvester W. Zhang.
Structure constants of Peterson Schubert calculus. Yuqi Jia, Xinkai Yu, Zhexi Zhang, Yuchen Zhu. Mentor: Tao Gui.
Winner of the 2025 ICCM Undergraduate Paper Award.

PACE 2024

Strong hull property of affine symmetric groups of rank 3. Ziming Liu, Shiyu Xiu. Mentor: Yibo Gao.
Hadamard products and compositional inverses of formal power series. Xuefan Chen. Mentor: Shaoshi Chen.
Higher continued fractions. Xuefan Chen, Shujian Li, Aiwer Liu, Junjie Ni. Mentor: Sylvester W. Zhang.
The isomorphism problem for adjoint and coadjoint Schubert varieties. Linji Chen, Yunhao Lai, Zhehan Xu. Mentor: Weihong Xu. FPSAC, poster.
On the Classification of Schubert Varieties in Partial Flag Varieties. Yanjun Chen. Mentor: Weihong Xu. FPSAC, poster.
Principal specializations of key polynomials. Yiwen Qiao, Kaixin Wang. Mentor: Neil J. Y. Fan.
Deodhar diagrams and rational Dyck paths. Yitong He, Muchen Ju, Kunyue Li, Aiwei Liu. Mentor: Peter L. Guo.
On Bott-Samelson rings for Coxeter groups. Lin Sun, Shihao Wang, Haoyu Zhu. Mentor: Tao Gui.
Clocks are e-positive. Luan Chen, Yitong He. Mentor: David G. L. Wang. Discrete Math. 349 (2026), no. 1, Paper No. 114723, 13 pp.
On the Vapnik-Chervonenkis dimensions of general linear groups and Artin braid groups. Luan Chen, Kunyue Li. Mentor: Kyle Gannon.
Hybrid Pipe Dreams for Key Polynomials. Yihan Xiao, Haofeng Zhang. Mentor: Rui Xiong. Adv. in Appl. Math. 173 (2026), part A, Paper No. 102979, 16 pp.
Arborescences of Random Covering Graphs. Muchen Ju, Junjie Ni, Kaixin Wang, Yihan Xiao. Mentor: Sylvester W. Zhang. FPSAC, poster.

PACE 2023

Dynamics on trapezoid posets. Yulin Peng, Zerui Xiang. Mentor: Sylvester W. Zhang.
Minimal face numbers of polytopes with 2d+2 vertices. Haoru Yang, Rongming Yin. Mentor: Lei Xue.
On the index of integer partitions. Mao Qian, Pengfei Yin, Hai Zhu. Mentor: Hui Sun.
Zero-one Grothendieck polynomial. Yiming Chen, Zelin Ye. Mentor: Neil J. Y. Fan.
Bounds on Schubert coefficients in the two-row case. Zijie Tao, Yunchi Zheng. Mentor: Yibo Gao.
Partial flag positroids. Zhixing Chen, Yumou Fei, Yuxuan Sun, Yuchong Zhang. Mentor: Jiyang Gao. FPSAC.
Properties of zeta map on Dyck paths. Yuchen Ge, Pengfei Yin, Hai Zhu. Mentor: Dun Qiu.
Full commutativity in complex reflection groups. Xuan Wang, Wei Wei, Haoru Yang. Mentor: Jiayuan Wang.
On the e-positivity of spiders with 3 legs. Yuchen Ge, Yulin Song, Zerui Xiang. Mentor: David G. L. Wang.
Expansion formulae for SL3 Fock–Goncharov cluster algebras. Ziyao Fu, Ni Tang, Yunchi Zheng. Mentor: Sylvester W. Zhang. FPSAC, poster.
Linearly independent products of Schur functions. Yuxuan Sun. Mentor: Shiliang Gao.
Hook formulas from Murnaghan-Nakayama rules Zhixing Chen, Rongming Yin. Mentor: Rui Xiong.
The monoid representation of upho posets and total positivity. Ziyao Fu, Yulin Peng, Yuchong Zhang. Mentor: Yibo Gao. FPSAC, poster.