Differential Geometry and Topology

course: Z2 and Z Deformation theory for holomorphic and symplectic manifolds

speaker: Paolo De Bartolomeis (Università di Firenze)

abstract: Deformation theories form one of the keystones of contemporary geometry, appearing in widely different areas and providing, through moduli space constructions, a highly powerful tool to produce new invariants. We first describe a tuning up of general machinery for deformation theory, enhancing relationships between the Z and Z2 theories.

Then, after presenting equivalence classes of Aoo-algebras as an example of deformation space, to exhibit the vast range covered by deformation theories, we deal with complexholomorphic deformations and symplectic deformation. In the latter case a totally new non-naive theory is constructed.

By means of the results established in the first part, both in the complexholomorphic case and the symplectic case, we define and discuss the corresponding Z2 theories (supercomplexholomorphic and supersymplectic structures).

timetable:
Tue 19 Oct, 17:00 - 18:15, Sala Conferenze Centro De Giorgi
Wed 20 Oct, 15:30 - 17:00, Sala Conferenze Centro De Giorgi
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