## Geometry Seminar - Abstracts

### Talk

Wednesday 12 December 2018, 16:00-17:00 in HG03.085

**Cary Malkiewich** (MPIM Bonn / Binghampton University)

*Periodic orbits and topological restriction homology*

### Abstract

I will talk about a project to import trace methods,
usually reserved for algebraic K-theory computations, into the study
of periodic orbits of continuous dynamical systems (and
vice-versa). Our main result so far is that a certain fixed-point
invariant built using equivariant spectra can be "unwound" into a
more classical invariant that detects periodic orbits. As a simple
consequence, periodic-point problems (i.e. finding a homotopy of a
continuous map that removes its n-periodic orbits) can be reduced to
equivariant fixed-point problems. This answers a conjecture of Klein
and Williams, and allows us to interpret their invariant as a class
in topological restriction homology (TR), coinciding with a class
defined earlier in the thesis of Iwashita and separately by
Luck. This is joint work with Kate Ponto.

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