The purpose of this book is to present the three basic ideas of geometrical probability, also known as integral geometry, in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. The first of the three ideas is invariant measures on polyconvex sets. The authors then prove the fundamental lemma of integral geometry, namely the kinematic formula. Finally the analogues between invariant measures and finite partially ordered sets are investigated, yielding insights into Hecke algebras, Schubert varieties and the quantum world, as viewed by mathematicians. Geometers and combinatorialists will find this a most stimulating and fruitful story.
We live in a period of uncertainty about the fate of American global leadership and the future of international order. The 2016 election of Donald Trump led many to pronounce the death, or at least terminal decline, of liberal international order - the system of institutions, rules, and values associated with the American-dominated international system. But the truth is that the unravelling of American global order began over a decade earlier. Exit from Hegemony develops an integrated approach to understanding the rise and decline of hegemonic orders. It calls attention to three drivers of transformation in contemporary order. First, great powers, most notably Russia and China, contest existing norms and values, while simultaneously building new spheres of international order through regional institutions. Second, the loss of the "patronage monopoly" once enjoyed by the United States and its allies allows weaker states to seek alternative providers of economic and military goods - providers who do not condition their support on compliance with liberal economic and political principles. Third, transnational counter-order movements, usually in the form of illiberal and right-wing nationalists, undermine support for liberal order and the American international system, including within the United States itself. Exit from Hegemony demonstrates that these broad sources of transformation - from above, below, and within - have transformed past international orders and undermine prior hegemonic powers. It provides evidence that that all three are, in the present, mutually reinforcing one another and, therefore, that the texture of world politics may be facing major changes""--
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