Combinatorial Algebraic Geometry
Combinatorial Algebraic Geometry

Author: Gregory G. Smith

Publisher: Springer

Published: 2017-11-17

Total Pages: 391

ISBN-13: 1493974866

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This volume consolidates selected articles from the 2016 Apprenticeship Program at the Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that ran from July through December of 2016. Written primarily by junior mathematicians, the articles cover a range of topics in combinatorial algebraic geometry including curves, surfaces, Grassmannians, convexity, abelian varieties, and moduli spaces. This book bridges the gap between graduate courses and cutting-edge research by connecting historical sources, computation, explicit examples, and new results.

Algebraic Methods in Statistics and Probability II
Algebraic Methods in Statistics and Probability II

Author: Marlos A. G. Viana

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 358

ISBN-13: 0821848917

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A decade after the publication of Contemporary Mathematics Vol. 287, the present volume demonstrates the consolidation of important areas, such as algebraic statistics, computational commutative algebra, and deeper aspects of graphical models. --

Computational Commutative Algebra 2
Computational Commutative Algebra 2

Author: Martin Kreuzer

Publisher: Springer Science & Business Media

Published: 2005-11-04

Total Pages: 592

ISBN-13: 3540282963

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"The second volume of the authors’ ‘Computational commutative algebra’...covers on its 586 pages a wealth of interesting material with several unexpected applications. ... an encyclopedia on computational commutative algebra, a source for lectures on the subject as well as an inspiration for seminars. The text is recommended for all those who want to learn and enjoy an algebraic tool that becomes more and more relevant to different fields of applications." --ZENTRALBLATT MATH

String-Math 2011
String-Math 2011

Author: Jonathan Block

Publisher: American Mathematical Soc.

Published: 2012

Total Pages: 506

ISBN-13: 0821872958

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The nature of interactions between mathematicians and physicists has been thoroughly transformed in recent years. String theory and quantum field theory have contributed a series of profound ideas that gave rise to entirely new mathematical fields and revitalized older ones. The influence flows in both directions, with mathematical techniques and ideas contributing crucially to major advances in string theory. A large and rapidly growing number of both mathematicians and physicists are working at the string-theoretic interface between the two academic fields. The String-Math conference series aims to bring together leading mathematicians and mathematically minded physicists working in this interface. This volume contains the proceedings of the inaugural conference in this series, String-Math 2011, which was held June 6-11, 2011, at the University of Pennsylvania.

An Introduction to Algebraic Statistics with Tensors
An Introduction to Algebraic Statistics with Tensors

Author: Cristiano Bocci

Publisher: Springer Nature

Published: 2019-09-11

Total Pages: 240

ISBN-13: 3030246248

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This book provides an introduction to various aspects of Algebraic Statistics with the principal aim of supporting Master’s and PhD students who wish to explore the algebraic point of view regarding recent developments in Statistics. The focus is on the background needed to explore the connections among discrete random variables. The main objects that encode these relations are multilinear matrices, i.e., tensors. The book aims to settle the basis of the correspondence between properties of tensors and their translation in Algebraic Geometry. It is divided into three parts, on Algebraic Statistics, Multilinear Algebra, and Algebraic Geometry. The primary purpose is to describe a bridge between the three theories, so that results and problems in one theory find a natural translation to the others. This task requires, from the statistical point of view, a rather unusual, but algebraically natural, presentation of random variables and their main classical features. The third part of the book can be considered as a short, almost self-contained, introduction to the basic concepts of algebraic varieties, which are part of the fundamental background for all who work in Algebraic Statistics.

Heights in Diophantine Geometry
Heights in Diophantine Geometry

Author: Enrico Bombieri

Publisher: Cambridge University Press

Published: 2006

Total Pages: 676

ISBN-13: 9780521712293

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This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.

An Introduction to Incidence Geometry
An Introduction to Incidence Geometry

Author: Bart De Bruyn

Publisher: Birkhäuser

Published: 2016-11-09

Total Pages: 380

ISBN-13: 3319438115

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This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end of the book. This book is aimed at graduate students and researchers in the fields of combinatorics and incidence geometry.