Mathematicians organized a topology conference for March 2016 in Baltimore to address their sense that algebraic topology, geometry, and category theory are in the midst of a generational shift of language, techniques, and paradigms rooting in new thinking about higher homotopy theory structures that profoundly alters the understanding of the nature of geometry and its applications across mathematics from data analysis to physics. These proceedings presents 10 papers on such aspects as the stable Galois correspondence for real closed fields, the Morita equivalence between parametized spectra and module spectra, the linearity of fixed-point invariants, homotopy coherent centers versus centers of homotopy categories, recent developments in noncommutative motives, and the category of Waldhausen categories as a closed multicategory. Annotation �2018 Ringgold, Inc., Portland, OR (protoview.com)

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