Time: 10:00
Speaker: Sajad Sadeghi (Western)
Title: "On Logarithmic Sobolev Inequality For the Noncommutative Two Torus and the Scalar Curvature Formula For the Noncommutative Three Torus"
Room: MC 106

Abstract: I will first give an overview of the noncommutative geometry. Then I will discuss

the classic Sobolev type inequalities and also the logarithmic Sobolev inequality and will compare them.

Moreover, one of the main results, which is the logarithmic Sobolev inequality on the noncommutative

two torus (NCT2), will be be proved for a class of elements in NCT2. Afterwards, I will introduce a family of

spectral triples, each of which represents a class of conformaly perturbed metrics on the noncommutative

three torus (NCT3) as a noncommutative compact spin manifold. Then using Connes' pseudodifferential

calculus, I will define the scalar curvature of NCT3 equipped with the mentioned conformaly perturbed

metrics and will compute it by an explicit formula.