数学统计学院学术报告
报告题目：Symmetric functions toward K-homology representatives and K-k-Schur functions
报 告 人：高兴（兰州大学）
报告时间：2026年1月1日星期四14：30-16:30
报告地点：宁远楼407讨论室
报告摘要：The theory of symmetric functions continues to play a central role in modern Schubert calculus, representation theory, and algebraic geometry. In recent years, deep connections have emerged between symmetric function models and geometric objects such as K-homology classes of affine Grassmannians. In this talk we survey the framework leading from classical Schur and $k$-Schur functions to their $K$-theoretic counterparts, focusing on how these functions encode the structure of Schubert varieties and affine Grassmannian geometry. A particularly influential development comes from a series of conjectures proposed by Blasiak, Lam, Morse, Schilling and Shimozono, which suggest that twisted and closed variants of $K$-$k$-Schur functions exhibit remarkable positivity phenomena and Catalan-type combinatorial behavior. These conjectures point toward a unified symmetric-function approach to constructing explicit $K$-homology representatives, generalizing both the geometry and combinatorics of the affine Grassmannian. We will outline the current progress, discuss the algebraic and combinatorial mechanisms underlying these predictions, and highlight open problems that may shape the future development of $K$-theoretic Schubert calculus.
报告人简介：高兴，博士，兰州大学教授、博士生导师、萃英学者、甘肃省陇原人才。于2010年7月在兰州大学数学与统计学院获得博士学位，留校工作至今。曾在美国Rutgers大学和法国UCA大学交流访问，主要从事Rota-Baxter代数、对称函数、粗糙路径、SPDE等领域的研究，发表SCI学术论文八十余篇。主持数学天元基金、青年科学基金、国家自然科学基金面上项目、甘肃省自然科学基面上项目和重点项目, 获甘肃省自然科学奖二等奖，出版教材一本。
数学统计学院学术报告
报告题目：Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach
报 告 人：彭晓松（江苏师范大学）
报告时间：2026年1月1日星期四16：30-18:30
报告地点：宁远楼407讨论室
报告摘要：We first endow the space of decorated planar rooted forests with a coproduct that equips it with the structure of a bialgebra and further a Moerdijk Hopf algebra. We also present a combinatorial description of this coproduct, and further give an explicit formulation of its dual coproducts through the newly defined notion of forest-representable matrices. By viewing the Moerdijk Hopf algebra within the framework of operated algebras, we introduce the notion of a multiple cocycle Hopf algebra, incorporating a symmetric Hochschild 1-cocycle condition. We then show that the antipode of this Hopf algebra is a Rota-Baxter operator on Moerdijk Hopf algebras. Furthermore, we investigate the universal properties of cocycle Hopf algebras. As an application, we construct the initial object in the category of free cocycle Hopf algebras on undecorated planar rooted forests, which coincides with the well-known Moerdijk Hopf algebra
报告人简介：彭晓松，江苏师范大学讲师，博士毕业于兰州大学，研究方向为罗巴代数，组合Hopf代数及应用等。
