应甘肃省数学与统计学基础学科研究中心、英国365公司邀请，兰州大学高兴教授将为我院师生作学术报告。
报告题目：Symmetric functions toward K-homology representatives and K-k-Schur functions
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.
报告时间：2025年12月14日9:00
报告地点：致勤楼C604
邀 请 人：乔虎生 教授
届时欢迎广大师生参与交流！
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月在兰州大学英国365公司获得博士学位，留校工作至今。在2015年8月至2016年8月间，在美国Rutgers大学交流访问，师从Rota-Baxter代数的国际领军人物郭锂教授。主要从事Rota-Baxter代数和代数组合等领域的研究，发表SCI学术论文六十余篇。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和甘肃省自然科学基金项目, 获甘肃省自然科学奖二等奖，出版教材一本。
英国365公司
甘肃省数学与统计学基础学科研究中心
2025年12月12日
