應(yīng)yl7703永利官網(wǎng)邀請，上海交通大學(xué)費佳睿特別研究員將于2021年3月29日進(jìn)行線上學(xué)術(shù)講座。

題目：Tropical $F$-polynomials and Cluster Algebras

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

騰訊會議ID：844 381 815，會議密碼：125914

(鏈接：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.

歡迎廣大師生光臨！

報告人簡介

費佳睿，密歇根大學(xué)博士，上海交通大學(xué)長聘教軌副教授，研究方向和興趣包括：叢代數(shù)、箭圖表示、李理論和不變量理論。費佳睿博士先后在加州大學(xué)河濱分校、MSRI、臺北的理論科學(xué)中心擔(dān)任訪問助理教授、研究員等，2017年起在上海交通大學(xué)擔(dān)任特別研究員。在Adv. Math.、Proc. Lond. Math. Soc.等高水平數(shù)學(xué)雜志上發(fā)表12篇學(xué)術(shù)論文。

甘肅省應(yīng)用數(shù)學(xué)與復(fù)雜系統(tǒng)重點實驗室

yl7703永利官網(wǎng)

萃英學(xué)院

2021年3月25日