Fouad El Zein – författare
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This book provides a comprehensive and up-to-date introduction to Hodge theory--one of the central and most vibrant areas of contemporary mathematics--from leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps. Of particular interest is the study of algebraic cycles, including the Hodge and Bloch-Beilinson Conjectures. Based on lectures delivered at the 2010 Summer School on Hodge Theory at the ICTP in Trieste, Italy, the book is intended for a broad group of students and researchers. The exposition is as accessible as possible and doesn't require a deep background. At the same time, the book presents some topics at the forefront of current research. The book is divided between introductory and advanced lectures. The introductory lectures address Kahler manifolds, variations of Hodge structure, mixed Hodge structures, the Hodge theory of maps, period domains and period mappings, algebraic cycles (up to and including the Bloch-Beilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendieck's algebraic de Rham theorem.The advanced lectures address a Hodge-theoretic perspective on Shimura varieties, the spread philosophy in the study of algebraic cycles, absolute Hodge classes (including a new, self-contained proof of Deligne's theorem on absolute Hodge cycles), and variation of mixed Hodge structures. The contributors include Patrick Brosnan, James Carlson, Eduardo Cattani, Francois Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, Le D?ng Trang, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.
Arrangements, Local Systems and Singularities
CIMPA Summer School, Galatasaray University, Istanbul, 2007
Inbunden, Engelska, 2009
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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.