In the representation theory of algebras, the study of subcategories of module categories has been one of the main topics, and is related to many areas. Among them, torsion classes and wide subcategories are important and have been studied by many people. In this talk, I will introduce the notion of ICE-closed subcategories of module categories, which are closed under taking Images, Cokernels and Extensions. This class contains both torsion classes and wide
subcategories. In the representation category of a Dynkin quiver, they bijectively correspond to rigid representations. For a general finite-dimensional algebra, I will explain how to classify ICE-closed subcategories using the poset structure of torsion classes, or using $\tau$-tilting theory. This talk is based on my joint work with Arashi Sakai (Nagoya).

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zoom URL: https://kyoto-u-edu.zoom.us/j/85442733050
passcode: The order of the Weyl group of type $E_6$