The Oberwolfach conference "Topologie" is one of only a few opportunities for researchers from many different areas in algebraic and geometric topology to meet and exchange ideas. This year we emphasized two topics of recent interest: representation stability and motivic homotopy theory, with their respective applications to arithmetic, classical homotopy theory as well as algebraic geometry. Double lectures on each topic where given by Benson Farb and Dan Isaksen. The rest of the program

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... d a wide range of topics ranging from topological Hochschild homology to obstruction theory of positive scalar curvature, via, to name a few, K-theory of C *algebras, modular characteristic classes, Goodwillie calculus, 2-Segal spaces and deformation quantization.