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Justin Curry : Studying Stratified Maps a la MacPherson

This talk is motivated by the question "Given a stratified map, how are path components of the fiber organized?" Studying path components necessitates cosheaves, but the stratified assumption provides an elegant combinatorial description using MacPherson's entrance path category, which also controls the associated Leray sheaves. One of the goals of this talk will be to provide a self-contained exposition of these ideas, using a minimal amount of mathematical background. The talk will follow loosely a recent paper with Amit Patel, which is available on the arXiv as http://arxiv.org/abs/1603.01587 Connections with applied topology will also be described.

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