Yibo Gao

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 2025

Due to various personal time commitment, PACE 2025 will be held primarily online. To apply for the program, please submit the following PDFs to pace@bicmr.pku.edu.cn:

• One recommendation letter sent directly by the letter writer to pace@bicmr.pku.edu.cn.
• A personal statement (max 2 pages) indicating your interests in the program.
• Your solutions to this test on combinatorics. (not yet available)
• Academic transcript.

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, Yanjun Chen, Yunhao Lai, Zhehan Xu. Mentor: Weihong Xu.
• 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. Tao Gui, Lin Sun, Shihao Wang, Haoyu Zhu. Mentor: Tao Gui.
• Clocks are e-positive. Luan Chen, Yitong He. Mentor: David G. L. Wang.
• 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.
• Covering graphs and expected value conjecture. Muchen Ju, Junjie Ni, Kaixin Wang, Yihan Xiao. Mentor: Sylvester W. Zhang.

PACE 2023

• Dynamics on trapezoid posets. Yulin Peng, Zerui Xiang, Sylvester W. Zhang. Mentor: Sylvester W. Zhang.
• Minimal face numbers of polytopes with 2d+2 vertices. Lei Xue, 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, Neil J. Y. Fan, Zelin Ye. Mentor: Neil J. Y. Fan.
• Bounds on Schubert coefficients in the two-row case. Zijie Tao, Yunchi Zheng. Mentor: Yibo Gao.
• Quotients of special classes of positroids. Zhixing Chen, Yumou Fei, Jiyang Gao, Yuxuan Sun, Yuchong Zhang. Mentor: Jiyang Gao.
• Properties of zeta map on Dyck paths. Yuchen Ge, Dun Qiu, 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, David G. L. Wang, Zerui Xiang. Mentor: David G. L. Wang.
• 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.