WORKSHOP: Non-Commutative Constructions in Arithmetic and Geometry

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It is little exaggeration to state that the mathematics of the twentieth century has made great advances through the study of commutative structures and linearization. This has been true both in the study of geometric structures and arithmetic ones. Meanwhile, partly through the intervention of ideas from physics, an increasing number of mathematicians have been struggling to extend the insights gained from commutative constructions to non-commutative structures, including non-abelian Galois theory and non-commutative differential and algebraic geometry. Such developments have been gradually coming to the fore over the last two decades in several regions of the world, including the UK, France, and Japan, partly in response to a grand research program proposed by the French mathematician Alexandre Grothendieck in the 80's. The time is then just right to plan ahead for a coherent vision of future research, where significant advances will depend on a sharing of vision and resources that cut across the boundary of disciplines and of nations. This workshop is a preliminary attempt to bring together world leaders in non-commutative constructions for in-depth discussion on future possibilities for collaboration, research, and the dissemination of ideas.