minicourse: Silting and tilting theory III

Abstract: This mini-course provides an introduction to the notion of a silting object in a triangulated category with coproducts, introduced independently by Psaroudakis and Vitória, and by Nicolás, Saorín and Zvonareva. We will see that silting objects correspond bijectively to certain triples formed by a t-structure and an adjacent co-t-structure. We will also discuss the dual notion of a cosilting object and the role of purity in this context. We will then present a notion of mutation for cosilting objects. Since our objects are not required to be compact, mutation is not always possible: it is controlled by proper-ties of certain torsion pairs in the heart of the associated t-structure. In the case of a two-term cosilting complex in the derived category of a finite dimensional algebra A, we will explain how these con-straints are reflected in the lattice torsA of all torsion pairs in the category modA formed by the finite dimensional A-modules.

The lectures will be based on joint work with Rosanna Laking, Frederik Marks, Jan Šťovíček and Jorge Vitória.

category theoryfunctional analysisrepresentation theory

Audience: researchers in the topic

( slides | video )

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Additive categories between algebra and functional analysis

Series comments: Aims & Scope: Exchange ideas and foster collaboration between researchers from representation theory and functional analysis working on categorical aspects of the theory. In addition to research talks, there will be four mini-courses of introductory character.

The instructions to join the meeting are available on the website: cats2021.github.io/ Registration is open.

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