My area of research is non-commutative geometry, where operator algebras meet differential geometry, topology and many other branches of mathematics. This field was introduced by Alain Connes in 1980’s, and since then it has grown very quickly. Non-commutative geometry is based on the idea that one can study geometric or topological properties of a space by looking at the function algebras on that space (these algebras are commutative). Exploiting this idea one can relax the commutativity condition and define non-commutative spaces through non-commutative algebras.

 

 

My Publications:

1)  A Scalar Curvature Formula for the Noncommutative Three Torus, joint with M. Khalkhali and A. Moatadelro, arXiv:1610.04740.

2)  On Logarithmic Sobolev Inequality for the Noncommutative Two Torus, joint with M. Khalkhali, J. Pseudo-Differ. Oper. Appl. Vol. 8, Issue 3, pp 453- 484 (2017).