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講演者：木村 嘉之　氏　（大阪市大）
題名: Quiver varieties and cluster algebras

日時：2013年5月11日（土）14:00〜17:00
場所：東京大学大学院・数理科学研究科117号室

アブストラクト:
Cluster algebras were introduced by Fomin and Zelevinsky with an aim
to provide concrete and combinatorial formalism for the study of
Lusztig's dual canonical basis and total positivity. Inspired by a
previous work of Nakajima, we consider a class of (equivariant)
perverse sheaves on acyclic graded quiver varieties and study the
Fourier-Sato-Deligne transform from a representation theoretic point
of view. In particular, we identifies the corresponding quantum
Grothendieck ring and the acyclic quantum cluster algebra (with
specific coefficients) and show that the set of quantum cluster
monomials is contained in the “dual canonical basis”.

In the first part, I will explain about the definition of cluster
algebra (of geometric type) , its positivity conjectures and their motivations.
In the second part, I will explain how the graded quiver varieties are
related with  cluster algebras and the positivity conjectures.

This talk is based on a joint work with Fan Qin(Tsinghua university).

なお、講演は日本語で行われます。

世話人: 岩尾慎介（青山学院大） 白石潤一（東大・数理） 土屋昭博（IPMU） 山田裕二（立教大）

セミナーURL : https://sites.google.com/site/seminaratkomaba/home

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岩尾慎介　青山学院数理
iwao at gem.aoyama.ac.jp