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Tuesday, February 11, 2020

**Abstract:** The Reidemeister trace of an endomorphism of a CW complex is a lower bound for the number of fixed points (up to homotopy) of that endomorphism. For an endomorphism $f$, the Reidemeister trace of $f^n$ is a lower bound for the number of fixed points of $f^n$, however it can be a far from an optimal lower bound. One method of addressing this discrepancy constructs an equivariant map, the n^{th} Fuller trace $f$, which carries information about the periodic points of a map $f$. However, we must ask how much information is retained by this equivariant construction? In this talk we show that the n^{th} Fuller trace of $f$ is a complete invariant for describing a minimum set of periodic points for maps of tori.