A combination of functional analysis with higher categories is essential for the mathematical understanding of quantum field theory, which is based on the fundamental principles of unitarity and locality. Locality is deeply tied to higher categorical structures, as is most explicit in the Atiyah-Segal approach to QFT through representations of the cobordism categories. On the other hand, the mathematical language of quantum mechanics and quantum field theory is functional analysis. 
This workshop brings together leading researchers--- from fields as disparate as analysis, higher categories, and rigorous QFT ---to arrive at a more complete theory.