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Lecture Series on Deformation Theory, January 12-27, 2016

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Six lectures on Deformation Theory by Peter Dalakov (Sofia)

What
  • Lecture Series
When Jan 12, 2016 10:15 AM to
Jan 27, 2016 12:00 PM
Where SR 318, SR 414
Contact Name
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This Lecture Series comprises six lectures on Deformation Theory by Peter Dalakov (Sofia). It starts with an overview lecture leading up to the approach to Deformation Theory via differential graded Lie algebras (DGLAs).

Please see below for a detailed schedule and description of the lectures (SR=seminar room):

 

12. Jan 2016, 10:15-12:00 (SR 318): Introduction and Motivation

Classification and moduli problems (global and local). Motivating examples:
families of Riemann surfaces of low genus; classification of topological vector bundles. The deformation functor.

 

15. Jan 2016, 14:15-16:00 (SR 318): Complex spaces. Families of compact complex manifolds

Reminder on complex spaces (in the sense of Grauert and Grothendieck), flatness. Families and morphisms of families,
(uni)versality.

 

19. Jan 2016, 10:15-12:00 (SR 318): Elements of Kodaira-Spencer theory. The Maurer-Cartan equation

Holomorphic vector fields, the Kodaira-Spencer map and its various interpretations. (Uni)versality criteria, Examples.
Semi-continuity and stability. Differential-geometric viewpoint on deformations of compact complex manifolds and the Maurer-Cartan equation.

 

22. Jan 2016, 14:15-16:00 (SR 318): Formal deformation theory

Functors of Artin rings, hulls and pro-representability, tangents spaces to functors, Schlessinger conditions. Examples. Remarks on the Bogomolov-Tian-Todorov theorem.

 

26. Jan 2016, 14:15-16:00 (SR 318): DGLA's

Deformation theory via DGLA's. Examples. Formal Kuranishi theory.


27. Jan 2016, 10:15-12:00 (SR 414): Further topics

Homotopy invariance of the Kuranishi space. Relation to Hodge theory. Further methods: DGBVA's/extended deformation functors/derived deformation theories.

 

 

 

 

 

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