Topology seminar

Abstract: This talk is about statistical field theories arising from observables which are homological in nature. Starting with a finite CW complex of dimension d, I will show how to construct a stochastic process in which the state space is given by integer-valued cellular (d-1)-cycles. A trajectory is given by a sequence of states equipped with waiting times, in which successive states are by joined by instantaneous jumps over d-cells. I will then construct a family of current observables and show how it gives rise to a real homology class in degree d called, "average current."

Lastly, I’ll discuss a fractional quantization result, which roughly says that if certain parameters driving the system (driving time, inverse temperature) tend to infinity, then the average current converges to a rational homology class.