邀请人：张海诚 副教授
腾讯会议：783926995
摘要：
Let $\Sigma$ be a Laurent phenomenon (LP) seed of rank $n$, $\mathcal{A}(\Sigma)$, $\mathcal{U}(\Sigma)$ and $\mathcal{L}(\Sigma)$ be its corresponding Laurent phenomenon algebra, upper bound and lower bound, respectively.
We prove that each seed of $\mathcal{A}(\Sigma)$ is uniquely defined by its cluster, and any two seeds of $\mathcal{A}(\Sigma)$ with $n-1$ common cluster variables are connected with each other by one step mutation. The method in this paper also works for (totally sign-skew-symmetric) cluster algebras. Moreover, we show that $\mathcal{U}(\Sigma)$ is invariant under seed mutations when each exchange polynomial coincides with its exchange Laurent polynomial of $\Sigma$. Besides, we obtain the standard monomial bases of $\mathcal{L}(\Sigma)$. We also prove that $\mathcal{U}(\Sigma)$ coincides with $\mathcal{L}(\Sigma)$ under certain conditions. This is a joint work with Qiuning Du.
报告人简介：李方, 浙江大学教授, 博士生导师，浙江大学高等数学研究所所长, 中国数学会理事。研究涉及代数领域的多个方面，在丛代数、Hopf代数、量子群、代数表示论和代数的拓扑方法上取得了代表性成果，研究成果发表于Adv. Math., Math. Ann., Compos. Math., J. Algebra等国内外重要学术期刊上。先后主持国家自然科学基金六项和浙江省自然科学基金重大和重点项目各一项。曾获浙江省高校科技进步一等奖等奖项，是国家教育部新世纪人才和浙江省151人才入选者。