Zhexi ZHANG, a 2022 undergraduate student in the Department of Mathematics at Southern University of Science and Technology (SUSTech), is the co-first author of a paper that has won the Sci-Tech Yangpu Undergraduate Paper Award at the 10th International Congress of Chinese Mathematicians (ICCM 2025). He has also been invited to deliver an academic report at Formal Power Series and Algebraic Combinatorics 2026 (FPSAC 2026), a top-tier international conference in the field of algebraic combinatorics.

The Peterson variety is a subvariety of the flag variety with profound geometric significance. Introduced by Dale Peterson, it is used to realize the quantum cohomology rings of all partial flag varieties. It is closely related to core areas such as the homology of the affine Grassmannian and the wonderful compactification of complex semisimple algebraic groups, and is a frontier object in the intersection of enumerative algebraic geometry and combinatorics. The core problem in Peterson Schubert calculus is to study the structure constants of the Peterson Schubert classes in the equivariant cohomology ring of the Peterson variety. These structure constants are polynomials defined over the integers, and their positivity was proven from a geometric perspective by Goldin, Mihalcea, Singh, and others, but for a long time, positive formulas were trailing behind. In 2011, Harada and Tymoczko posed an open problem to find positive formulas in type A, and since then, this problem has not been fully solved for all Lie types.

The research team, using a purely algebraic method based on Cartan matrices, provided for the first time explicit formulas for all equivariant structure constants in arbitrary Lie types. These formulas depend solely on the Cartan matrix of the corresponding root system and are characterized by simplicity, positivity, and type uniformity. As an application, the team also derived type-uniform formulas for mixed Eulerian numbers in arbitrary Lie types.

The paper lists Tao GUI from Beijing International Center for Mathematical Research, Yuqi JIA from Qiuzhen College, Tsinghua University, Xinkai YU from University of Science and Technology of China, Zhexi ZHANG from SUSTech, and Yuchen ZHU from Nankai University as co-first authors (in alphabetical order by surname), with Tao GUI as the corresponding author, and SUSTech as a co-first author institution.

The 10th International Congress of Chinese Mathematicians is organized by the Shanghai Institute for Advanced Studies in Mathematics and Interdisciplinary Research (SIMIS). The congress awards several important prizes, including the ICCM Sci-Tech Yangpu Undergraduate Paper Award (2025), which aims to recognize undergraduates who demonstrate outstanding creativity and research potential in mathematical research.

FPSAC (Formal Power Series and Algebraic Combinatorics) conferences, initiated in 1988, are among the oldest and most influential annual international academic conferences in the field of algebraic combinatorics. The 38th FPSAC conference will be held in July 2026 at the University of Washington, USA.

Paper Link: https://arxiv.org/abs/2508.05457