Dmitriy Zanin (University of New South Wales)
Title: Dao of the principal symbol
Abstract: We introduce a principal symbol mapping as a bounded *homomorphism of C*-algebras. Connes Trace Formula is stated and proved
in terms of the introduced notion of a principal symbol. The core idea and
technique applies not only to the space $\mathbb{R}^d$, but also to
noncommutative plane $\mathbb{R}^d_{\theta}$, commutative and
noncommutative tori, commutative and noncommutative spheres, quantum
group SU(q,2) and many other important examples.