Graded Algebras, Algebraic Functions, Planar Trees, and Elliptic Integrals; Prof. Vesselin Drensky
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The starting point of the talk is how to measure how big an infinite dimensional algebra is. In particular, we discuss the problem how to construct graded algebras with prescribed Hilbert series, including Hilbert series which are algebraic but not rational. It has turned out that this problem concerns not only algebra. It is related with interesting problems in graph theory (enumeration of graphs with prescribed properties), mathematical analysis (e.g., theory of algebraic and transcendental functions). Even elliptic integrals surprisingly appear as Hilbert series of naturally looking (nonassociative) algebras.