
Noncommutative Geometry, Cyclic Cohomology, and Hopf Algebras
Masoud Khalkhali, University of Western Ontario, Canada


Abstract:
In these lectures I will explain the basic intuitive idea
behind noncommutative geometry, in the sense of A. Connes, as a duality
between geometric and algebraic objects. Many notions
and invariants of geometric and topological nature have their
counterparts in noncommutative geometry. In particular cyclic homology
is the noncommutative analogue
of de Rham cohomology of smooth manifolds. It pairs with both
topological and algebraic Ktheory of noncommutative algebras. I will
explain how a special class of noncommutative and noncocommutative Hopf
algebras naturally appeared in noncommutative geometry in the work of
Connes and Moscovici on local index formula for foliated manifolds. The
last parts of these lectures will be devoted to current work on the
cyclic cohomology of Hopf algebras.
These lectures are meant to be a gentel introduction to the ideas
involved and should be accessible to graduate students and postdoctoral
fellows and those who are interested. I will make sure to provide the
necessary background material during the lectures.
Detail Schedule:

Introduction to noncommutative geometry
Saturday, April 10, 15:0017:00 
Ktheory, cyclic cohomology and ChernConnes character
Saturday, April 17, 15:0017:00 
Hopf algebras in noncommutative geometry and
transverse index theory of ConnesMoscovici
Saturday, April 24, 15:0017:00 
Place: School of Mathematics, Niavaran Bldg., Niavaran Square, Tehran, Iran. 

See some photos 
 
