I warmly invite you to attend the following short course:

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Speaker: Bernhard Keller (Université de Paris)

Title: Hochschild (co-)homology of differential graded categories.

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Lecture I: Hochschild (co-)homology of differential graded categories I.

Date: 19 November 2021 (Friday) at 11:00-12:00 (London time).

Abstract: We will start with a reminder on derived categories and derived functors including Rickard's Morita theorem for derived categories. We will conclude with a short proof of derived invariance of Hochschild homology based on the formalism developed so far.

Video: Lecture I

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Lecture II: Hochschild (co-)homology of differential graded categories II.

Date: 26 November 2021 (Friday) at 11:00-12:00 (London time).

Abstract: We will examine the functoriality properties of Hochschild cohomology under derived functors. Then we will recall the higher structure present on the Hochschild cochain complex itself and show that it is preserved under derived equivalences and also under less stringent hypotheses. We will then enlarge the framework to include dg (=differential graded) categories.

Video: Lecture II

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Lecture III: Hochschild (co-)homology of differential graded categories III.

Date: 3 December 2021 (Friday) at 11:00-12:00 (London time).

Abstract: We will sketch how to extend all previous invariance results to Hochschild (co-)homology of dg categories. We will apply this in the study of singular (=Tate-) Hochschild cohomology, which we will compare with the Hochschild cohomology of (dg) singularity categories. We will conclude with a review of reconstruction results for singularities obtained in joint work with Zheng Hua.

Video: Lecture III

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Notes: Lectures I, II and III

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Organizer: Goncalo Tabuada