Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Gröbner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics.
Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel–Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.
Brendan Cummins has made more senior hurling championship appearances than any other player in the history of the game. In an era that produced such brilliant goalkeeping talents as Davy Fitzgerald, Donal Óg Cusack and Damien Fitzhenry, many would argue that Cummins has earned the right to be considered the greatest of them all. Following his League debut for Tipperary in November 1993, Cummins went on to play at the top of the intercounty game for 19 consecutive seasons. He won two senior All Ireland medals, five Munster championships, four League titles and five All Star awards. From fearless shot-stopping to pinpoint accuracy on his puck-outs, Cummins was unrivalled in the consistency of his performances, a consistency underpinned by a sometimes punishing physical commitment, mental discipline and great attention to detail. He was the rock upon which Tipperary built their team under many managers and changes of personnel. Brendan Cummins' story is the story of Tipperary hurling over the last two decades. The ups and downs. The dramas. The characters. From his senior championship debut in 1995 under Fr. Tom Fogarty to his final games under Eamon O’Shea, Cummins has seen it all. Standing My Ground is a remarkable account of an extraordinary career.
What's so special about Thomond Park? The crowd. Simply the crowd. The atmosphere is electric.' Donal Spring, one of Munster rugby's greatest. Since the first game played there in 1934, Thomond Park has become one of the world's iconic rugby venues. It is a magnificent stadium, famous for many great occasions, notably Munster's 1978 victory over the All Blacks and the 'Miracle Match' against Gloucester in 2003. It also has a worldwide reputation for tradition, wit and an outstanding sense of fair play. Here the history of Thomond Park is traced in a colourful and entertaining style, featuring some rare photos of Munster favourite Paul O'Connell, and highlighting great games played and great characters who have graced the arena.
This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel–Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.
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