[Binghamton Geometry/Topology Seminar] Cary Malkiewich

[jwilliams at math.binghamton.edu]

Speaker: Cary Malkiewich

Title: Periodic points and equivariant stable homotopy theory

Abstract: The Lefschetz number L(f) and Reidemeister trace R(f) are
invariants that detect fixed points of a map f: X -> X. I will talk about
the generalizations of these invariants that detect n-periodic points of
f, and an ongoing project with Kate Ponto that involves showing that
periodic-point problems and equivariant fixed-point problems are
controlled by the same invariants. Along the way we will see some
equivariant stable homotopy theory, and some arguments that amount to
``unwinding'' a string to show that a more complicated invariant reduces
to a simpler one. These arguments allow us to resolve a conjecture of
Klein and Williams; it still remains to connect them to related work of
Geoghegan and Nicas on flows.

Thursday Nov. 9, 2:50pm, WH-100E