OxTalks will soon move to the new Halo platform and will become 'Oxford Events.' There will be a need for an OxTalks freeze. This was previously planned for Friday 14th November – a new date will be shared as soon as it is available (full details will be available on the Staff Gateway).
In the meantime, the OxTalks site will remain active and events will continue to be published.
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Accessibility percolation is a simple model in evolutionary biology describing how a population driven by the evolutionary forces of selection and mutation explores a fitness landscape. Mathematically, the fitness landscape is modeled by attaching random weights to the vertices of a graph.
Then, accessible percolation asks whether there are paths of increasing fitness of a certain length. I will review some of the progress in this area and then consider the question what happens if the fitness landscape changes over time. In particular, I will focus on the case when the underlying graph is a regular tree. Depending on the ratio of depth to width of the tree, we will see different scaling regimes for the time it takes to see an increasing path. Some of the proofs rely on adapting techniques from the area of noise sensitivity for Boolean functions.
