Dima Gurevich (Valenciennes University, France)

Title: Elements of Braided Geometry

Abstract: Braided Geometry means a "non-commutative geometry"  based on a generalized (quantum) permutation, which can be  associated with a solution of the Quantum Yang-Baxter Equation (the braiding). Many notions of the classical and super-geometries can be naturally generalized in this frameworks. I am going to  discuss the braided analogs of the (super-)traces, Lie (super-) algebras, (super-)vector fields etc. Also, I am planning to present recent results concerning braided analogs of oirbits in gl(n)* and  explain how a quantization of certain Poisson brackets gives rise to braided objects.