Colloquium

Speaker: Jason Lotay (University College, London, UK)

"Adventures in 7 dimensions"

Time: 11:00

Room: MC 107

Ricci-flat spaces are analogues of space-times satisfying Einstein's vacuum field equations of General Relativity. Unlike their flat cousins, these spaces exhibit fascinating geometric properties and are poorly understood. In odd dimensions the only non-trivial Ricci-flat spaces we can find are 7-dimensional and they appear in theoretical physics, making geometry in 7 dimensions particularly compelling to study. I will describe in an elementary way some of the recent endeavours to understand this geometry and several key open questions.

Noncommutative Geometry

Speaker: Jeremie Gauthier (Western)

"The Inverse spectral problem for regular n gons"

Time: 15:00

Room: MC 107

Colloquium

Speaker: George Elliott (Toronto)

"The agony and the ecstasy: the classification of unital simple amenable C*-algebras"

Time: 11:00

Room: MC 107

After an enormous amount of work by many authors (perhaps two thousand pages), it has been shown that every unital simple separable C*-algebra satisfying certain natural hypotheses (finite nuclear dimension, and the Universal Coefficient Theorem---the latter possibly redundant) is a limit of type I C*-algebras, and that these can be classified by simple invariants. The non-unital case looks promising, but may still require a considerable amount of work.

PhD Thesis Defence

Speaker: Sajad Sadeghi (Western)

"On Logarithmic Sobolev Inequality For the Noncommutative Two Torus and the Scalar Curvature Formula For the Noncommutative Three Torus"

Time: 14:00

Room: MC 107

I will first discuss

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

Moreover, one of my 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.