#### Alladi Ramakrishnan Hall

#### Coarse geometry for noncommutative spaces

#### Tathagata Banerjee

##### Goettingen

*In the talk we shall mainly be interested in looking at quantization using Rieffel*

deformation by actions of $\mathbb{R}^d$ through coarse geometry. Coarse geometry is

concerned with the large scale aspect of the topology of a space and we know that

quantum physics is equivalent to classical physics when considered at large

distances. We define noncommutative coarse structures on a non-unital

$C^\ast$-algebra in terms of its unitizations and develop a particular notion of a

noncommutative coarse map. Coarse structures given by proper metrics are the most

interesting examples of classical coarse geometry, and can be equivalently defined

in terms of its Higson compactification. We use this and our theory of

noncommutative coarse geometry to show equivalence between the metric coarse

structure of the classical plane $\mathbb{R}^{2n}$ and its Rieffel deformation, the

Moyal plane. Finally if time permits, we shall look into further examples of

noncommutative coarse maps and equivalences. This has been my Ph.D. project under

Prof. Ralf Meyer.

Done