Gerard B.M. van der Geer's Books

The 1-2-3 of Modular Forms

Lectures at a Summer School in Nordfjordeid, Norway

By: Jan Hendrik Bruinier,Gerard van der Geer,Günter Harder,Don Zagier

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The 1-2-3 of Modular Forms

Lectures at a Summer School in Nordfjordeid, Norway

By: Jan Hendrik Bruinier,Gerard van der Geer,Günter Harder,Don Zagier

This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.

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Page Count

273

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540741194

ISBN 13

9783540741190

Hilbert Modular Surfaces

By: Gerard van der Geer

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Hilbert Modular Surfaces

By: Gerard van der Geer

Over the last 15 years important results have been achieved in the field of Hilbert Modular Varieties. Though the main emphasis of this book is on the geometry of Hilbert modular surfaces, both geometric and arithmetic aspects are treated. An abundance of examples - in fact a whole chapter - completes this competent presentation of the subject. This Ergebnisbericht will soon become an indispensible tool for graduate students and researchers in this field.

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Page Count

301

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642615538

ISBN 13

9783642615535

Error Propagation in Environmental Modelling with GIS

By: Gerard B.M. Heuvelink

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Error Propagation in Environmental Modelling with GIS

By: Gerard B.M. Heuvelink

GIS users and professionals are aware that the accuracy of GIS results cannot be naively based on the quality of the graphical output. Data stored in a GIS will have been collected or measured, classified, generalised, interpreted or estimated, and in all cases this allows the introduction of errors.; With the processing of translation of this data into the GIS itself further propagation or amplification or errors also occur. It is essential that GIS professionals understand these issues systematically if they are to build ever more accurate systems.; In this book the authors decade of study into these problems is brought into focus with an account of the development, application and implementation of error propagation techniques for use in environmental modelling with GIS. Its purpose is to provide a methodology for handling error and error propagation.

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Page Count

156

Publisher

CRC Press

Published Date

ISBN 10

0748407448

ISBN 13

9780748407446

The Moduli Space of Curves

By: R. Dijkgraaf,Carel Faber,Gerard B.M. van der Geer

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The Moduli Space of Curves

By: R. Dijkgraaf,Carel Faber,Gerard B.M. van der Geer

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. Leading experts in the field explore in this volume both the structure of the moduli space of curves and its relationship with physics through quantum cohomology. Altogether, this is a lively volume that testifies to the ferment in the field and gives an excellent view of the state of the art for both mathematicians and theoretical physicists. It is a persuasive example of the famous Wignes comment, and its converse, on "the unreasonable effectiveness of mathematics in the natural science." Witteen’s conjecture in 1990 describing the intersection behavior of tautological classes in the cohomology of Mg arose directly from string theory. Shortly thereafter a stunning proof was provided by Kontsevich who, in this volume, describes his solution to the problem of counting rational curves on certain algebraic varieties and includes numerous suggestions for further development. The same problem is given an elegant treatment in a paper by Manin. There follows a number of contributions to the geometry, cohomology, and arithmetic of the moduli spaces of curves. In addition, several contributors address quantum cohomology and conformal field theory.

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Page Count

584

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817637842

ISBN 13

9780817637842

Book's by Gerard B.M. van der Geer

The 1-2-3 of Modular Forms

The 1-2-3 of Modular Forms

Hilbert Modular Surfaces

Hilbert Modular Surfaces

Error Propagation in Environmental Modelling with GIS

Error Propagation in Environmental Modelling with GIS

The Moduli Space of Curves

The Moduli Space of Curves

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