Lecure 1: Dualities in Non Commutative Geometry
Date and Time: Sunday, August 5, 2012 at 10:0011:00
Lecure 2: Cyclic Homology and Applications
Date and Time: Sunday, August 5, 2012 at 11:1512:15
Slide Show 1
Lecure 3: Hopf Algebras and Hopf Cyclic Cohomology
Date and Time: Monday, August 6, 2012 at 10:0011:00
Lecure 4: HopfGalios Extensions
Date and Time: Monday, August 6, 2012 at 11:1512:15
Slide Show 2
Abstract
Noncommutative geometry asserts that the category of algebras
(commutative or noncommutative)of various flavors is operationally the
category of spaces (commutative or noncommutative) of
various flavors. This duality leads to build a dictionary to translate
important concepts from one category to the other. In the first session we
shortly review some of these dualities such as GelfandNeimark, SerreSwan
and Connes reconstruction theorems. In the second talk we study an
important subject in noncommutative geometry called cyclic cohomology
which carries out interesting geometrical, topological and algebraic
information. Next we survey the basics of Hopf cyclic cohomology which
was discovered by Connes and Moscovici in 1998 in the course of
their breakthrough analysis of transverse index theory
on foliated spaces. Finally in the last lecture, we study Hopf Galois
extensions of algebras which generalizes the classical Galois
extensions of fields and also the notion of principal bundles. We
introduce some new results in this subject.
Information:
 Place:  Niavaran Bldg., Niavaran Square, Tehran, Iran 
