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https://msri.zoom.us/s/585445592

We will describe new combinatorial structures arising at the intersection of stratified topology, singularity theory and algebraic higher category theory. These combinatorial structures locally classify stratifications that are transversal with respect to an ambient foliation structure. As two applications of the resulting correspondence between combinatorics and geometry we will construct a stratification of the space of tangles (inspired by ideas from Morse, Cerf, and singularity theory) and define a combinatorial theory of 'higher string diagrams' in arbitrary dimension.

Transversal Stratifications