Persistent homology is a central object of study in applied topology. It offers a flexible framework for defining invariants, called barcodes, of point cloud data and of real valued functions. Many of the key results of the last several years in the theory of persistent homology have been formulated in terms of a metric on barcodes called the bottleneck distance. There is a multi-parameter generalization of persistent homology, called multi-dimensional persistent homology, which is naturally suited to the study of noisy point cloud data.
We will discuss the notion of loops in linguistic structures, mainly in dictionaries. In a simplified view, a dictionary is a graph that links every word (vertex) to a set of alternative words (the definition) which in turn point to further descendants. Iterating through definitions, one may loop back to the original word. We will examine possible links between such definitional loops and the emergence of new concepts during the evolution of languages. Potential relation to living systems will be briefly discussed.
10:00 am - 11:00 am Melissa Liu, Columbia University, "Coherent-constructible correspondence and homological mirror symmetry II"
11:30 am - 12:30 pm Mohammed Abouzaid, MIT, "Generation criteria for the Fukaya category II"