Abstract

I introduce certain class of (noncommutative) quadratic algebras which happened to be connected with numerous fields of Mathematics such as Algebra, Representation Theory, Algebraic Combinatorics, Graph Theory, Low Dimensional Topology, Classscal and Quantum Schubert and 

Grothendieck Calculi, Special Functions, and Integrable Systems, and hopefully with many others. In my talk I'm planning to explain some elementary properties of that algebras ,such as connections with Catalan and Fuss-Catalan numbers, triangulations and dissections of a convex n-gon, and Schubert Calculus. The main purpose of my talk is to draw attention of the audience to this  Subject.