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After a brief introduction to the basic concepts of entanglement in discrete and continuous systems I will outline various results of our recent work in these areas. In particular, I will present a scaling relation for the entanglement of a subsystem with respect to the rest of the lattice in the size of the regions.

The abstract can be found at http://www.city.ac.uk/sems/mathematics/seminars.html

Chosen aspects of twisted brane geometry in the Wess-Zumino-Witten models of type A_2n shall be discussed, both classical and stringy, in reference to a class of coideal subalgebras of Drinfel'd-Jimbo quantum groups known as twisted orthogonal quantum groups. An explicit relation between the two families of algebras, together with a realisation of the latter as (twisted) Reflection Equation Algebras shall be invoked to emphasise the role played by them in a compact algebraic description of quantum twisted branes on SU(2n+1) in the framework of R-matrix Reflection Equations and associated quantum group geometries.

The talk shall present chosen aspects of a compact quantum-algebraic description of D-brane geometry in WZW models, extending beyond the semiclassical approximation of the original fuzzy matrix models. It shall be argued that a class of unital algebras - the so-called Reflection Algebras intimately related to Drinfeld--Jimbo algebras - captures certain essential features of stringy geometries, both untwisted and twisted, in compact WZW models and their (simple current) orbifolds, while giving rise to some well-known, and some less so, noncommutative geometries (e.g. Podles sphere, quantum projective plane).