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. This volume covers a broad range of topics in mathematical physics, including noncommutative geometry, supergeometry, derived symplectic geometry, higher geometric quantization, intuitionistic quantum logic, problems with the continuum description of spacetime, twistor theory, loop quantum gravity, and geometry in string theory. It is addressed primarily to mathematical physicists and mathematicians, but also to historians and philosophers of these disciplines.

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.

Gabriel Catren is a philosopher and a physicist working at the Institut SPHERE--Science, Philosophie, Histoire (Universite Paris Diderot--CNRS, Paris).The great poets and thinkers of modernity described a situation we still inhabit today: the catastrophic undermining of all foundations, the disorienting relativization of all reference points, the prospect of abandonment to chance and contingency alone--the shipwreck of Mallarme's Coup de des. In this precise and poetic work of philosophy, Gabriel Catren sketches out a new "phenoumenodelic" solution to this momentous ungrounding, defiantly refusing both unrestrained contingency and arbitrary refoundation. Mobilizing a formidable knowledge of the major currents of modern thought, deftly articulating Kantian transcendentalism and Spinozan immanentism, phenomenological reduction and scientific realism, Catren argues that the projects oriented by the infinite ideas of reason (Truth, Beauty, Justice, Love) need not be abandoned in the face of the "exquisite crisis" of modernity. Instead, the "shipwreck" is to be understood as a suspension of finite subjectivity in the fullness of a "phenoumenodelic pleroma," an atonal milieu ringing with unheard-of possibilities. Announcing an ambitious program for the renewal of transcendental philosophy, in Pleromatica Catren recomposes the primary elements of modern thought into a startling new configuration, introducing a vivid constellation of new concepts with which to map out and navigate the vast space of this "worldless daydream."

After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. These books 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. They are addressed primarily to mathematicians and mathematical physicists, but also to historians and philosophers of these disciplines.