Positivity and polytope basis in cluster algebras via Newton polytopes

讲座时间 Datetime: 2022年6月10日，星期五， 16:00 -17:30

地点 Venue: 腾讯线上会议：946-628-9201

 主持人 Host：黄敏

报告人 Speaker:潘杰

单位 Affiliation:浙江大学

报告摘要 Abstract:

We work in the generality of a totally sign-skew-symmetric cluster algebra of rank $n$. We study the Newton polytopes of $F$-polynomials and, more generally, a family of polytopes $N_h$ indexed by vectors $h$ in $Z^n$. We use it to give a new proof of Laurent positivity and to construct what we call the polytope basis of the upper cluster algebra. The polytope basis consists of certain universally indecomposable Laurent polynomials. It is strongly positive and generalizes the greedy basis constructed by Lee-Li-Zelevinsky in rank 2. This is a report on joint work with Fang Li, cf. arXiv:2201.01440