After the development of manifolds and algebraic varieties in the
previous century, mathematicians and physicists have continued to
advance concepts of space. This book and its companion explore
various new notions of space, including both formal and conceptual
points of view, as presented by leading experts at the New Spaces
in Mathematics and Physics workshop held at the Institut Henri
Poincare in 2015. The chapters in this volume cover a broad range
of topics in mathematics, including diffeologies, synthetic
differential geometry, microlocal analysis, topos theory,
infinity-groupoids, homotopy type theory, category-theoretic
methods in geometry, stacks, derived geometry, and noncommutative
geometry. It is addressed primarily to mathematicians and
mathematical physicists, but also to historians and philosophers of
these disciplines.
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