Algebraic $K$-theory has seen a fruitful development during the last three years. Part of this recent progress was driven by the use of $\infty$-categories and related techniques originally developed in algebraic ...

Algebraic $K$-theory and motivic cohomology have developed together over the last thirty years. Both of these theories rely on a mix of algebraic geometry and homotopy theory for their construction and development, and ...

Algebraic K-theory and the related motivic cohomology are a systematic way of producing invariants for algebraic or geometric structures. Its definition and methods are taken from algebraic topology, but it has also proved ...

Riemannian manifolds with positive scalar curvature play an important role in mathematics and general relativity. Obstruction and existence results are connected to index theory, bordism theory and homotopy theory, using ...

The investigation of Riemannian metrics with lower scalar curvature bounds has been a central topic in differential geometry for decades. It addresses foundational problems, combining ideas and methods from global analysis, ...

The purpose of this Arbeitsgemeinschaft was to study and—as far as possible—compare three generalisations of the classical Franz-Reidemeister torsion to families E → B of manifolds. Dwyer, Weiss and Williams construct ...

Introduced by Bökstedt-Hsiang-Madsen in the nineties, topological cyclic homology is a manifestation of the dual visions of Connes-Tsygan and Waldhausen to extend de Rham cohomology to a noncommutative setting and to ...

The field of operator algebras is a flourishing area of mathematics with strong ties to many other areas including functional/harmonic analysis, topology, (non-commutative) geometry, group theory and dynamical systems. The ...

The purpose of the workshop was to bring together mathematicians interested in ”quantization of manifolds” in a broad sense: given classical data, such as a Lie group G acting on a symplectic manifold M, construct a quantum ...