REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

Anton Khoroshkin

ABSTRACT: The core of the talk consists of the combinatorial construction of free resolutions for algebraic objects that are defined in terms of generators and relations. For the case of associative algebras the procedure looks as follows (first due to Anick): one should describe the combinatorics of the minimal resolution of a monomial replacement and deform the differential afterwords. A similar construction exists whenever the notion of monomial replacement is well defined. My particular interests are in the theory of operads which I hope to provide with several interesting examples.