Starts 27 Oct 2016 17:00
Ends 27 Oct 2016 18:00
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Derived deformation theory of noncommutative spaces
ICTP
Leonardo Building - Luigi Stasi Seminar Room
Abstract:
One of the powerful feature of derived algebraic geometry is to enlighten deformation theory. We will explain this point of view from scratch, and review the main results of derived deformation theory by Lurie. In a second part, I'll explain how this can be applied to the deformation theory of noncommutative spaces in the sense of Kontsevitch, i.e. differential graded categories. In general this theory is badly behaved, but under some finiteness condition on the category (in particular it has a compact generator), we prove together with Katzarkov and Pandit that every formal deformation still has a compact generator.
One of the powerful feature of derived algebraic geometry is to enlighten deformation theory. We will explain this point of view from scratch, and review the main results of derived deformation theory by Lurie. In a second part, I'll explain how this can be applied to the deformation theory of noncommutative spaces in the sense of Kontsevitch, i.e. differential graded categories. In general this theory is badly behaved, but under some finiteness condition on the category (in particular it has a compact generator), we prove together with Katzarkov and Pandit that every formal deformation still has a compact generator.