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Riemann Surfaces and Algebraic Curves
Classroom-tested and featuring over 100 exercises, this text introduces the key algebraic geometry field of Hurwitz theory.
Tropical and Logarithmic Methods in Enumerative Geometry
This book is based on the lectures given at the Oberwolfach Seminar held in Fall 2021. Logarithmic Gromov-Witten theory lies at the heart of modern approaches to mirror symmetry, but also opens up a number of new directions in enumerative geometry of a more classical flavour. Tropical geometry forms the calculus through which calculations in this subject are carried out. These notes cover the foundational aspects of this tropical calculus, geometric aspects of the degeneration formula for Gromov-Witten invariants, and the practical nuances of working with and enumerating tropical curves. Readers will get an assisted entry route to the subject, focusing on examples and explicit calculations.
Legitimacy and Effectiveness in Global Economic Governance
Coping with the challenges of global economic governance is a topical issue of the current international agenda, and the object of a vivid debate among scholars and policy-makers. The international financial and economic crisis that erupted in 2007 reveals the fallibility of the neoliberal paradigm that has dominated the world economic landscape for the last quarter of a century; regulatory and supervisory institutions have disclosed their weaknesses, and markets have shown their limits in dealing with the rational allocation of risks, and their lack of resilience to shocks. This book offers a comprehensive view of this matter, examining the dialectic and fluid relations between State sovere...
Topological Recursion and its Influence in Analysis, Geometry, and Topology
This volume contains the proceedings of the 2016 AMS von Neumann Symposium on Topological Recursion and its Influence in Analysis, Geometry, and Topology, which was held from July 4–8, 2016, at the Hilton Charlotte University Place, Charlotte, North Carolina. The papers contained in the volume present a snapshot of rapid and rich developments in the emerging research field known as topological recursion. It has its origin around 2004 in random matrix theory and also in Mirzakhani's work on the volume of moduli spaces of hyperbolic surfaces. Topological recursion has played a fundamental role in connecting seemingly unrelated areas of mathematics such as matrix models, enumeration of Hurwit...
TRIPS and Developing Countries
TRIPS reflects the dominant view that enforcing strong intellectual property rights is necessary to solve problems of trade and development. The global ensemble of authors in this collection ask, how can TRIPS mature further into an institution that su
Effective Faithful Tropicalizations Associated to Linear Systems on Curves
For a connected smooth projective curve X of genus g, global sections of any line bundle L with deg(L) ≥ 2g + 1 give an embedding of the curve into projective space. We consider an analogous statement for a Berkovich skeleton in nonarchimedean geometry: We replace projective space by tropical projective space, and an embedding by a homeomorphism onto its image preserving integral structures (or equivalently, since X is a curve, an isometry), which is called a faithful tropicalization. Let K be an algebraically closed field which is complete with respect to a nontrivial nonarchimedean value. Suppose that X is defined over K and has genus g ≥ 2 and that Γ is a skeleton (that is allowed to have ends) of the analytification Xan of X in the sense of Berkovich. We show that if deg(L) ≥ 3g − 1, then global sections of L give a faithful tropicalization of Γ into tropical projective space. As an application, when Y is a suitable affine curve, we describe the analytification Y an as the limit of tropicalizations of an effectively bounded degree.
Welfare, Environment and Changing US-Chinese Relations
Scholars of political economy and international economics as well as academics and researchers of Asian - particularly Chinese- studies, will find this book of great value. Since the People's Republic of China began to promote an open-door policy to foreign investment in 1979, economic results have been startling. In twenty years China recorded at least eight percent growth in gross domestic product annually. Since 1978 the number of Chinese living in poverty dropped from 270 million to 60 million. China's economy cou. By adopting a wide-ranging perspective, this book addresses the key issues relevant to contemporary China, providing a valuable tool with which to understand the challenges an...
States, Actors and Geopolitical Drivers in the Mediterranean
Moving from a historical and cultural perspective, this book examines the geo-political and socio-economic changes involving the enlarged Mediterranean. Organised into two main sections, the first section (The new centrality of the Mediterranean Basin: Trends and Dynamics) is devoted to the analysis of the most relevant drivers and interdisciplinary broader issues, and the second section (Hotspots of Crisis and Regional Interferences in the Mediterranean) assesses the situation in some areas interested by the waves of uprisings since 2011-12. The book aims to uncover this new, critical centrality of the Mediterranean in the global scenario through the analysis of the interactions and intertwining of those trends and dynamics offering a historical holistic broad view. What follows is an Italian perspective that is the result of the research of a group of scholars who have been working for years on the first-hand sources of the countries examined. A peculiar vision connected not only to its unique geographical position at the center of the basin, but also to its deep relations with the southern shore throughout its long history.
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