欢迎进入 兰州大学数学与统计学院

当前位置: 首页 > 学术交流 > 正文

“九章讲坛”第304讲 — 费佳睿 研究员

日期:2021-03-25点击数:

应数学与统计学院邀请,上海交通大学费佳睿特别研究员将于2021年3月29日进行线上学术讲座。

题目:Tropical $F$-polynomials and Cluster Algebras

时间:2021年3月29日(周一),下午15:00—16:00 (北京时间)

腾讯会议ID:844 381 815,会议密码:125914

(链接:https://meeting.tencent.com/s/2cHfLPZzvB81)

摘要:The $g$-vectors and $F$-polynomials are two fundamental ingredients in the (additive) categorification of cluster algebras. We knew that the $g$-vectors are related to the presentation spaces. We introduce the tropical $F$-polynomial $f_M$ of a quiver representation $M$. We study its interplay with the general presentation for any finite-dimensional basic algebra.

To be more specific, we give an interpretation of evaluating $f_M$ at a weight vector. As a consequence, we give a presentation of the Newton polytope $N(M)$ of $M$. We propose an algorithm to determine the generic Newton polytopes, and show it works for path algebras. As an application, we give a representation-theoretic interpretation of Fock-Goncharov's duality pairing.

We also study many combinatorial aspects of $N(M)$, such as the dual fan and 1-skeleton. We conjecture that the coefficients of a cluster monomial corresponding to vertices are all 1, and the coefficients inside the Newton polytope are saturated. We show the conjecture holds for acyclic cluster algebras. We specialize the above general results to the cluster-finite algebras and the preprojective algebras of Dynkin type.

欢迎广大师生光临!

报告人简介

费佳睿,密歇根大学博士,上海交通大学长聘教轨副教授,研究方向和兴趣包括:丛代数、箭图表示、李理论和不变量理论。费佳睿博士先后在加州大学河滨分校、MSRI、台北的理论科学中心担任访问助理教授、研究员等,2017年起在上海交通大学担任特别研究员。在Adv. Math.、Proc. Lond. Math. Soc.等高水平数学杂志上发表12篇学术论文。


甘肃省应用数学与复杂系统重点实验室

数学与统计学院

萃英学院

2021年3月25日