REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

Anton Khoroshkin

ABSTRACT: It is well known that the generating function of a generic finitely presented algebra is rational. The purpose of this talk is to present an answer to a similar question in the case of operads.  Namely, I will show that the generating series of a generic nonsymmetric operad is an algebraic function and the generating series of a generic symmetric operad is differentially algebraic. All results are based on the combinatorics of trees/monomials and are provided with algorithms that might be useful in particular computation.  Despite the motivation coming from the operad theory, a substantial part of the talk will only deal with the combinatorics of tree monomials and hence will be accessible to nonspecialists. Based on joint work with D.Piontkovsky