NCG Seminar announcement

[Emanuele Tuillier Illingworth]

NON COMMUTATIVE GEOMETRY SEMINAR ANNOUNCEMENT


Dr. Francesco D'Andrea (Univ. of Naples)

Modules over the noncommutative torus, elliptic curves and cochain 
quantization

16:00, Friday 21 Nov 2014,
SISSA, room 136


The non-commutative torus is commonly described as a cocycle 
quantization of the group (C^*-)algebra of the abelian group Z^2. In the 
first part of the talk I will explain how, using the WBZ transform of 
solid state physics, finitely generated projective modules over the 
NC-torus can be interpreted as deformations of vector bundles on 
elliptic curves by the action of a 2-cocycle, provided that the 
deformation parameter of the NC-torus and the modular parameter of the 
elliptic curve satisfy a non-trivial relation. I will then discuss the 
relation between (formal) deformations of vector bundles on the torus 
and cochain twists based on the Lie algebra of the 3-dimensional 
Heisenberg group. Based on a joint work with G. Fiore and D. Franco.