Lecture Series on Deformation Theory, January 1227, 2016
Six lectures on Deformation Theory by Peter Dalakov (Sofia)
What 


When 
Jan 12, 2016 10:15 AM
to Jan 27, 2016 12:00 PM 
Where  SR 318, SR 414 
Contact Name  Florian Beck 
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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, 10:1512:00 (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, 14:1516:00 (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, 10:1512:00 (SR 318): Elements of KodairaSpencer theory. The MaurerCartan equation
Holomorphic vector fields, the KodairaSpencer map and its various interpretations. (Uni)versality criteria, Examples.
Semicontinuity and stability. Differentialgeometric viewpoint on deformations of compact complex manifolds and the MaurerCartan equation.
22. Jan 2016, 14:1516:00 (SR 318): Formal deformation theory
Functors of Artin rings, hulls and prorepresentability, tangents spaces to functors, Schlessinger conditions. Examples. Remarks on the BogomolovTianTodorov theorem.
26. Jan 2016, 14:1516:00 (SR 318): DGLA's
Deformation theory via DGLA's. Examples. Formal Kuranishi theory.
27. Jan 2016, 10:1512:00 (SR 414): Further topics
Homotopy invariance of the Kuranishi space. Relation to Hodge theory. Further methods: DGBVA's/extended deformation functors/derived deformation theories.