Texas A&M Workshop in Analysis and Probability: Geometry and Analysis on Nonsmooth Spaces

The goal of this in-person conference is to bring together researchers studying nonsmooth spaces from different perspectives, facilitating the exchange of ideas, problems, and mathematical techniques. Perspectives coming from probability, analysis on metric spaces, and Banach space theory are of particular emphasis. Interactions among these different fields have already proven exceptionally fruitful. For example, a famous fractal space constructed by Laakso to answer a purely metric measure theoretic question inspired a similar construction (pictured above) eventually used to characterize superreflexivity in Banach spaces. Later, uniform q-convexity, a quantitative refinement of superreflexivity, was metrically characterizing using Markov convexity – a measurement of the diffusivity of Markov processes in a metric space. Together with many more examples, these show how shared geometric objects play important roles in each subject while being viewed through different lenses. More interactions of this type will be necessary to solve important open problems, such as analyst’s traveling salesman-type problems and metric characterizations of other Banach properties.