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Within the past five years, non-commutative geometry as well as derived and super geometry have become a powerful tool in the mathematics of quantum field theory. 
Sheaf methods, disk quantization techniques, and tropical enumerative geometry have found new applications in mathematics and in the study of quantum fields and strings. 
The influx of new mathematical ideas has led to a profound new understanding of a range of physical and mathematical dualities including classical string dualities, 
large N duality, homological mirror symmetry, geometric engineering, and symplectic duality.  
This RISM school will allow for the review of recent advances in homotopical aspects of geometry and their applications to various moduli spaces by leading experts. 
In addition, the conference seeks to facilitate further expansion of these techniques into the realm of supersymmetric gauge theory and quantum field theory.

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