# Manchester Geometry Seminar 2015/2016

**Friday 29 April 2016 (non-standard day). ** *The Lamb Room (Room 1.204), the Alan Turing Building. 4.15pm*
##
Quantum Matrix Algebras and Their Applications

Dimitri Gourevitch (Université de Valenciennes)

`dimitri.gurevich@gmail.com`

By quantum matrix algebras I mean algebras related to quantum groups
and close in a sense to that $\mathop{Mat}(m)$. These algebras have numerous
applications. In particular, by using them (more precisely, the so-called
reflection equation algebras) we succeeded in defining
partial derivatives on the enveloping algebras $U(\mathfrak{gl}(m)$). This enabled us to
develop a new approach to Noncommutative Geometry: all objects of this type geometry
are deformations of their classical counterparts. Also, with the help
of the reflection equation algebras we introduced the notion of braided
Yangians, which are natural generalizations of the usual ones and have
many beautiful properties.