# Analysis, Geometry, and Dynamical Systems Seminar

## Past sessions

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### Remarks about diffusion mediated transport

Diffusion mediated transport is implicated in the operation of many molecular level systems. These include some liquid crystal and lipid bilayer systems, and, especially, the motor proteins responsible for eukaryotic cellular traffic. All of these systems are extremely complex. In this expository talk we address the basic elements of transport in an environment of diffusion, concentrating on the flashing rachet. We illustrate how to characterize the properties of this process in terms of a Markov chain. It is of essential importance to understand what it means to determine a Markov chain in this manner, namely, the sense in which the discrete problem is an accurate description of the original continuous one. Here we are able to exploit some novel concepts about the dynamics of evolutionary systems including an appeal to the classical Monge transfer problem. This perspective illuminates the fundamental connection between the two problems and presents an opportunity for future applications.

This is joint work with Michal Kowalczyk.

### Linking of geodesic spheres in dimension 2

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