Quantisation of Super Teichmüller Theory

Quantisation of Twistor Theory by Cocycle Twist

We present the main ingredients of twistor theory leading up to and including the Penrose-Ward transform in a coordinate algebra form which we can then ‘quantise’ by means of a functorial cocycle twist. The quantum algebras for the conformal group, twistor space CP3, compactified Minkowski space CM and the twistor correspondence space are obtained along with their canonical quantum differential...

Teichmüller Shape Space Theory and Its Application to Brain Morphometry

Here we propose a novel method to compute Teichmiiller shape space based shape index to study brain morphometry. Such a shape index is intrinsic, and invariant under conformal transformations, rigid motions and scaling. We conformally map a genus-zero open boundary surface to the Poincaré disk with the Yamabe flow method. The shape indices that we compute are the lengths of a special set of geo...

Semiclassical Methods of Deformation Quantisation in Transport Theory

Quantum Teichmüller Space

We describe explicitly a noncommutative deformation of the *-algebra of functions on the Teichmüller space of Riemann surfaces with holes equivariant w.r.t. the mapping class group action.

Comparison between Teichmüller

The Teichmüller distance between two points σ, τ in Teichmüller space T (S) is defined in terms of the minimal quasiconformal constantK(σ, τ) between σ and τ . In [10] Thurston introduced an analogous metric on T (S) by considering the least possible value of the global Lipschitz constant Λ(σ, τ) from σ to τ . On the one hand, Kerckhoff [3] showed that K(σ, τ) can be formulated in terms of the ...