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Title: Graded Algebras, Algebraic Functions, Planar Trees, and
       Elliptic Integrals

Speaker: Prof. Vesselin Drensky
        (Institute of Mathematics and Informatics,
         Bulgarian Academy of Sciences, Sofia, Bulgaria)

Time and Location: Wednesday, October 23, 2019, 2 p.m.;
                   RISC Seminarroom, Hagenberg castle.

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.