Geometry of the Moyal-Weyl type noncommutative spaces and star products. Uses of Moyal type non-commutative space in quantum physics and quantum field theory. UV-IR mixing in noncommutative field theories and its consequences.
Description of fuzzy spaces and their properties, examples of the fuzzy sphere , their geometrical properties. Structure of the fuzzy complex projective spaces
Classical field theories over the fuzzy sphere. Scalar and spinor fields, the Laplace and the Dirac operator on .
Topologically nontrivial configurations on fuzzy spaces, complex line bundles over fuzzy spaces and their geometrical description.
Abelian and non-abelian gauge theories on . Steinacker’s random matrix model formulation. Monopole sectors of fuzzy gauge theories.
Description of non-linear sigma models over and .
Dynamical generation of fuzzy spaces in certain gauge theories and string related matrix models
Matrix models in string theory and M-theory. BMN models and its fuzzy vacuum configurations.
Fuzzy 4-sphere, its geometrical properties and uses in Yang-Mills matrix models.
Survey of future directions and discussion of research ideas.