Gustavo Jasso 3/4 - The Derived Auslander-Iyama Correspondence
Автор: GeoTopCPH
Загружено: 2026-02-06
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In this lecture series we will study the general question of when the quasi-isomorphism type of a differential graded algebra A is uniquely determined by its graded cohomology algebra H*(A) plus a 'minimal' amount of additional data. We will focus on the case where A enjoys a strong regularity property as a generator of its perfect derived category, the so-called dZ-cluster tilting property. We will also study the case where, in addition, the differential graded algebra A is bimodule right Calabi-Yau.
In slightly more detail, the aim of the lecture series is to explain how techniques of homotopy theory can be leveraged to prove certain classification results of interest in representation theory---the Derived Auslander--Iyama Correspondence of the title and its bimodule Calabi--Yau variant---that seem to be out of reach by other methods. If time permits, we will also explain, following Keller, an application of these results to the (first) affirmative solution of the Donovan--Wemyss Conjecture in the context of Wemyss' Homological Minimal Model Programme in birrational geometry.
This lecture series is based on an ongoing project with Fernando Muro (Sevilla).
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