Algebraic geometry

The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinoya Rorbuer, Svolvaer in Lofoten, in August 2017, present both survey and research articles on the recent surge of developments in understanding moduli problems in algebraic geometry.

This textbook on Feynman integrals starts from the basics, requiring only knowledge of special relativity and undergraduate mathematics.

A tribute to the vision and legacy of Israel Moiseevich Gelfand, the invited papers in this volume reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory.

This bookprovides an overview of the latest developments concerning the moduli of K3surfaces.

The goal of Geometric Algebra Applications Vol.

B.

This two-volume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923 - 1998).

In this book the authors describe the important generalization of the original Weil conjectures, as given by P.

This unique collection of new and classical problems provides full coverage of algebraic inequalities.

The common solutions of a finite number of polynomial equations in a finite number of variables constitute an algebraic variety.

The present monograph further develops the study, via the techniques of combinatorial anabelian geometry, of the profinite fundamental groups of configuration spaces associated to hyperbolic curves over algebraically closed fields of characteristic zero.

In recent years there has been enormous activity in the theory of algebraic curves.

This volume contains the proceedings from the first Women in MathArt Research Collaboration Conference for Women, showcasing women mathematicians researching and curating creative pedagogies at the intersection of mathematics and the arts.

Elementary number theory is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q.

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory.

This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated.

Comprehensive account of theory and applications of Gröbner bases, co-edited by the subject''s inventor.

This book presents the state of the art on numerical semigroups and related subjects, offering different perspectives on research in the field and including results and examples that are very difficult to find in a structured exposition elsewhere.

This book offers a review of the vibrant areas of geometric representation theory and gauge theory, which are characterized by a merging of traditional techniques in representation theory with the use of powerful tools from algebraic geometry, and with strong inputs from physics.

Resolution of singularities is notorious as a difficult topic within algebraic geometry.

Particles with fractional statistics interpolating betweenbosons and fermions have attracted considerable interestfrom mathematical physicists.

Recent Progress of Algebraic Geometry in Japan

This book lays out the theory of Mordell-Weil lattices, a very powerful and influential tool at the crossroads of algebraic geometry and number theory, which offers many fruitful connections to other areas of mathematics.

Differential algebraic groups were introduced by P.

The aim of the present monograph is to give a systematic exposition of the theory of algebraic surfaces emphasizing the interrelations between the various aspects of the theory: algebro-geometric, topological and transcendental.

Functional Analysis: Surveys and Recent Results

Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.

This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case.

This text introduces students to an experimental approach to mathematics, using Maple to systematically investigate and develop mathematical theory.

This book consists of five chapters presenting problems of current research in mathematics, with its history and development, current state, and possible future direction.

The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud.

Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry.

The first contribution covers the theory of finite groups of Lie type, which is an important field of current mathematical research.

These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant theory associates to reductive group actions on nonsingular complex projective varieties.

The goal of this textbook is to introduce and study automorphic representations, objects at the very core of the Langlands Program.

Vector Measures and Control Systems

The present monograph is a state-of-art survey of the geometry of matrices whose study was initiated by L K Hua in the forties.

The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y.

A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.

The second of two volumes offering a modern account of Kaehlerian geometry and Hodge theory for researchers in algebraic and differential geometry.

This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout.

Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics.

This encyclopedia presents an all-embracing collection of analytical surface classes.

This book deals with two subjects.

New mathematical research in arithmetic dynamicsIn The Arithmetic of Polynomial Dynamical Pairs, Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics.

The general problem studied by information theory is the reliable transmission of information through unreliable channels.