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An Invitation to Modern Enumerative Geometry
This book is based on a series of lectures given by the author at SISSA, Trieste, within the PhD courses Techniques in enumerative geometry (2019) and Localisation in enumerative geometry (2021). The goal of this book is to provide a gentle introduction, aimed mainly at graduate students, to the fast-growing subject of enumerative geometry and, more specifically, counting invariants in algebraic geometry. In addition to the more advanced techniques explained and applied in full detail to concrete calculations, the book contains the proofs of several background results, important for the foundations of the theory. In this respect, this text is conceived for PhD students or research “beginne...
L'ultimo marinaio
Una storia di mare. Una storia di amicizia. Una storia di vita. «Andrea Ricolfi si fa notare per una scrittura che sceglie la levità anche nello stile. Un esordio notevole. » Avvenire - Fulvio Panzeri «Ne «L’ultimo marinaio» si percepisce, nitida, l’urgenza di pensare a un’umanità bella. Speriamo che Andrea Ricolfi scriva ancora. » ttL - La Stampa - Lidia Ravera «A un certo punto, su questo oceano e per le piccole strade di Noss, è passato un uomo singolare, che ha portato un po’ di limpidezza nella mia vita. Tomas Henkel, questo era il suo nome, mi ha insegnato a scorgere la nobiltà nei sotterranei sentieri delle anime in cui talvolta si nasconde, a intuire la profondità...
Lectures on Nonsmooth Differential Geometry
This book provides an introduction to some aspects of the flourishing field of nonsmooth geometric analysis. In particular, a quite detailed account of the first-order structure of general metric measure spaces is presented, and the reader is introduced to the second-order calculus on spaces – known as RCD spaces – satisfying a synthetic lower Ricci curvature bound. Examples of the main topics covered include notions of Sobolev space on abstract metric measure spaces; normed modules, which constitute a convenient technical tool for the introduction of a robust differential structure in the nonsmooth setting; first-order differential operators and the corresponding functional spaces; the theory of heat flow and its regularizing properties, within the general framework of “infinitesimally Hilbertian” metric measure spaces; the RCD condition and its effects on the behavior of heat flow; and second-order calculus on RCD spaces. The book is mainly intended for young researchers seeking a comprehensive and fairly self-contained introduction to this active research field. The only prerequisites are a basic knowledge of functional analysis, measure theory, and Riemannian geometry.
Intellectual Property Law and Human Rights
Human rights issues arise more and more often in an intellectual property context. ' Intellectual property and human rights' is the first comprehensive analysis of this emerging nexus of legal issues. In twenty-one incisive essays, well-known authorities in both intellectual property law and human rights law present in-depth analysis and discussion of such essential topics as the following: The human rights credentials of copyright and other intellectual property rights; The relations between copyright and freedom of speech and of expression, from the perspectives of both North American and European law; The relevance to copyright of the public interest defence in European law; The way trade...
The Moduli Space of Curves
The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.
Geometry of Moduli Spaces and Representation Theory
This book is based on lectures given at the Graduate Summer School of the 2015 Park City Mathematics Institute program “Geometry of moduli spaces and representation theory”, and is devoted to several interrelated topics in algebraic geometry, topology of algebraic varieties, and representation theory. Geometric representation theory is a young but fast developing research area at the intersection of these subjects. An early profound achievement was the famous conjecture by Kazhdan–Lusztig about characters of highest weight modules over a complex semi-simple Lie algebra, and its subsequent proof by Beilinson-Bernstein and Brylinski-Kashiwara. Two remarkable features of this proof have i...
The Geometry of Moduli Spaces of Sheaves
This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds
In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical...
