Date: 13 September 2019
Location: Hempfield High School, Room 213
 Speaker: Jeremy Brazas, West Chester University
 Title: Infinitary operations in fundamental groupoids

 Abstract: The are many natural situations where a group with
some additional structure admits an infinitary operation, i.e. some kind
of infinite sum or product. Fundamental groups and groupoids of
topological spaces with non-trivial local structure (e.g. the Hawaiian
earring, Menger Curve, and Sierpinski Carpet) provide natural models of
algebraic structures with non-commutative infinite product
operations. Since the 1990’s, significant progress has been made in the
development and application of these topological-algebraic objects,
culminating in Eda’s remarkable homotopy classification of
one-dimensional Peano continua. In this talk, I’ll give an introduction
to this area and discuss why even knowing that these infinitary
operations are well-defined on homotopy classes is not always clear.