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Geometry --- Mathematics --- landmeetkunde --- functies (wiskunde) --- wiskunde
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This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)". The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern points of view on Galois theory and related moduli problems, using stacks, gerbes and groupoids. It contains lecture notes on étale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articles complete the collection.
Group theory --- Algebraic geometry --- Geometry --- Mathematics --- Classical mechanics. Field theory --- landmeetkunde --- wiskunde --- mechanica --- geometrie
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This volumecomprisesa setof lecturenotes fromthe CIMPASummer School,- rangements and Local systems and Singularities, held at Galatasaray University, Istanbul,during June11-22,2007.Theschoolwasattendedby68mathematicians, 35 of them from 19 countries outside Turkey. The Summer School was made up of eleven short courses and ?ve seminars presented by an outstanding group of lecturers who covered a wide range of topics related to the concepts of arran- ments, localsystems andsingularities.Thelist of lectures ofthe workshopappears below.Mostmembers of the audienceweregraduatestudents oryoung researchers and the primary purpose of the school was to introduce them, in particular those from developing countries, to the many advances and opportunities in this widely applicable ?eld. Historically,researchonarrangementsofhyperplanes,starting with the work of V.I. A'rnold and E. Brieskorn and later Peter Orlik, was presented at meetings devoted mainly to discussions of singularities. Some of the articles in this volume demonstratethattheinteractionbetweenthesetwosubjectsis ongoingandpart- ularly productive. Beyond this, the volume is intended for a largeaudience in pure mathematics, including researchers and graduate students working in algebraic geometry, singularity theory, topology and related ?elds. The reader will ?nd in the ProblemSection at the end of the volumea variety of open problems proposed by the lecturers at the end of the School's sessions as directions ripe for further study and development.
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This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results of a problem session. Key topics are moduli spaces of points on P1 and Picard-Terada-Deligne-Mostow theory, moduli spaces of K3 surfaces, complex hyperbolic geometry, ball quotients, GKZ hypergeometric structures, Hilbert and Picard modular surfaces, uniformizations of complex orbifolds, algebraicity of values of Schwartz triangle functions, and Thakur's hypergeometric function. The book provides a background, gives detailed expositions and indicates new research directions. It is directed to postgraduate students and researchers.
Geometry --- Mathematics --- landmeetkunde --- functies (wiskunde) --- wiskunde
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This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results of a problem session. Key topics are moduli spaces of points on P1 and Picard-Terada-Deligne-Mostow theory, moduli spaces of K3 surfaces, complex hyperbolic geometry, ball quotients, GKZ hypergeometric structures, Hilbert and Picard modular surfaces, uniformizations of complex orbifolds, algebraicity of values of Schwartz triangle functions, and Thakur's hypergeometric function. The book provides a background, gives detailed expositions and indicates new research directions. It is directed to postgraduate students and researchers.
Mathematics. --- Algebraic geometry. --- Special functions. --- Special Functions. --- Algebraic Geometry. --- Math --- Science --- Special functions --- Mathematical analysis --- Algebraic geometry --- Geometry --- Functions, special. --- Geometry, algebraic. --- Algebra --- Geometry, Algebraic --- Number theory
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