[Binghamton Geometry Topology Seminar] Geometry and Topology seminar: John Klein

[Cary Malkiewich]

Hi everyone,

Correction: we will be taking the topology speaker to dinner on *Wednesday*
night instead of Thursday, since he's catching a plane back on Thursday.
Please let me know if you would like to come!

Cary

On Mon, Mar 9, 2020 at 1:06 PM Cary Malkiewich <
malkiewich at math.binghamton.edu> wrote:

> Hi everyone,
>
> This week we are very pleased to have John Klein (Wayne State University)
> speaking in the geometry and topology seminar. The title and abstract are
> below. As usual, the talk is at 2:50pm in WH-100E.
>
> Please let me know if you would like to come to the dinner after!
>
> Cheers,
> Cary
>
> =========================================
> Title: Hypercurrents
> Abstract: This talk poses the question as to what a higher dimensional
> analog of a continuous time Markov chain might be, in which the time
> parameter is replaced by arbitrary smooth manifold.
>
> As a partial answer, we introduce the notion of a “protocol,” which
> consists of a space whose points are labeled by real numbers indexed by the
> set of cells of a fixed CW complex in prescribed degrees, where the labels
> are required to vary continuously. When the space is a one-dimensional
> manifold, then a protocol determines a continuous time Markov process.
>
> In the presence of a homological gap condition, we associate to each
> protocol a ‘characteristic’ cohomology class which we call the
> hypercurrent. The hypercurrent comes in two flavors: one algebraic
> topological and the other analytical. For generic protocols we show that
> the analytical hypercurrent tends to the topological hypercurrent in the
> 'low temperature' limit.
>
> We also exhibit examples of protocols having nontrivial hypercurrent.
>
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