His topics include groups and

homogeneous spaces, the extended Fillmore-Springer-Cnops construction, the indefinite product space of cycles, metric invariants in upper half-planes, conformal unit disk, and unitary rotations.

Specifically, we are going to study such problems as the local index formula, equivariance of Dirac operators with respect to the dual group action (with an eye towards the Baum-Connes conjecture for discrete quantum groups), construction of Dirac operators on quantum

homogeneous spaces, structure of quantized C*-algebras of continuous functions, computation of dual cohomology of compact quantum groups.

He discusses special and general relativity and the cosmological versions of both, properties of the gravitational field, particle production in five-dimensional cosmological relativity, properties of gravitational waves in an expanding universe, spiral galaxy rotation curves in the Brane world theory in five dimensions, testing cosmological general relativity against high redshift observations,

homogeneous spaces and Bianchi classifications, and similar topics.

His topics include invariant connections on reductive

homogeneous spaces, finite order isometries and twistor spaces, vertically harmonic maps and harmonic sections of submersions, generalized harmonic maps, and generalized harmonic maps into f-manifolds and into reductive

homogeneous spaces.

Because in reality there do not exist isolated

homogeneous spaces, but a mixture of them, interconnected, and each having a different structure.

Some topics examined are superrigidity and first applications, locally

homogeneous spaces, and orbit equivalence.

Workshop on Several Complex Variables, Analysis on Complex Lie Groups and

Homogeneous Spaces (2005: Hangzhou, China)

This new field of research, which is closely allied to Kahlerian geometry, is also related to affine differential geometry,

homogeneous spaces and cohomology.

He begins by providing a foundation in quasigroups and loops, multiplication groups and central quasigroups, moving to

homogeneous spaces, permutation representations, character tables, combinational character theory, schemes and superschemes, permutation characters, modules, and applications of module theory, closing with a description of analytical character theory, providing exercises and problems for each topic.

He covers topological Lie algebras, Lie groups and their Lie algebras, enlargeability, smooth

homogeneous spaces, quasimultiplicative maps, complex structures in

homogeneous spaces, equivariant monotone operators, L*-ideals and equivariant monotone operators,

homogeneous spaces of pseudo-restricted groups.

Coverage then progresses from Jordan decomposition through

homogeneous spaces and quotients.

2: Set of recorders are called a

homogeneous space of recorders, if all its elements equally receive all signals.