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サイエンスフロンティア（数学専攻主催）開講情報　

10/24, 10/31, 11/7　Dr. Bernard Leclerc

　下記の通り、サイエンスフロンティア（数学専攻主催）を開講いたします。

講師紹介

　　Bernard Leclerc 名誉教授Caen 大学　　

　　専門分野：表現論

講義タイトル

　　Introduction to cluster algebras and monoidal categorifications.

講義内容　

I'd like to give three lectures as follow:Lecture 1 : Definition of cluster algebras. Basic examples and results. Its topics are: Cluster seed. Seed mutation. Examples. Laurent phenomenon. Finite-type classification. A main reference is T. Nakanishi, https://arxiv.org/pdf/2201.11371, Sections 1, 2, 3. Lecture 2 : Monoidal categorification of type A cluster algebras via representations of quantum affine sl(2). Its topics are: Monoidal categorification. Definition of U_q(sl_2^). Evaluation representations. Classification of simple finite-dimensional modules. Type A cluster structure on monoidal subcategories of mod(U_q(sl_2^)). A main reference is D. Hernandez, B. Leclerc, https://arxiv.org/pdf/1902.01432, Sections 1, 2. Lecture 3 : Cluster algebras and module categories of quantum affine algebras. Its topics are: Quantum affine algebras of type A, D, E and their finite-dimensional representations. Kirillov-Reshetikhin modules. T-systems. HL-subcategories. Cluster structure on HL-subcategories. A main reference is D. Hernandez, B. Leclerc, https://arxiv.org/pdf/1902.01432, Sections 3, 4, 5.

講義日程、場所

10月24日（木）3限

10月31日（木）3限

11月7日（木）3限

理学部E棟408（杉本）

担当者：宮地兵衛