Interactions of Classical and Numerical Algebraic Geometry

Interactions of Classical and Numerical Algebraic Geometry
Author :
Publisher : American Mathematical Soc.
Total Pages : 379
Release :
ISBN-10 : 9780821847466
ISBN-13 : 0821847465
Rating : 4/5 (66 Downloads)

Synopsis Interactions of Classical and Numerical Algebraic Geometry by : Daniel James Bates

This volume contains the proceedings of the conference on Interactions of Classical and Numerical Algebraic Geometry, held May 22-24, 2008, at the University of Notre Dame, in honor of the achievements of Professor Andrew J. Sommese. While classical algebraic geometry has been studied for hundreds of years, numerical algebraic geometry has only recently been developed. Due in large part to the work of Andrew Sommese and his collaborators, the intersection of these two fields is now ripe for rapid advancement. The primary goal of both the conference and this volume is to foster the interaction between researchers interested in classical algebraic geometry and those interested in numerical methods. The topics in this book include (but are not limited to) various new results in complex algebraic geometry, a primer on Seshadri constants, analyses and presentations of existing and novel numerical homotopy methods for solving polynomial systems, a numerical method for computing the dimensions of the cohomology of twists of ideal sheaves, and the application of algebraic methods in kinematics and phylogenetics.

Hodge Theory and Classical Algebraic Geometry

Hodge Theory and Classical Algebraic Geometry
Author :
Publisher : American Mathematical Soc.
Total Pages : 148
Release :
ISBN-10 : 9781470409906
ISBN-13 : 1470409909
Rating : 4/5 (06 Downloads)

Synopsis Hodge Theory and Classical Algebraic Geometry by : Gary Kennedy

This volume contains the proceedings of a conference on Hodge Theory and Classical Algebraic Geometry, held May 13-15, 2013, at The Ohio State University, Columbus, OH. Hodge theory is a powerful tool for the study and classification of algebraic varieties. This volume surveys recent progress in Hodge theory, its generalizations, and applications. The topics range from more classical aspects of Hodge theory to modern developments in compactifications of period domains, applications of Saito's theory of mixed Hodge modules, and connections with derived category theory and non-commutative motives.

Facets of Algebraic Geometry

Facets of Algebraic Geometry
Author :
Publisher : Cambridge University Press
Total Pages : 395
Release :
ISBN-10 : 9781108792516
ISBN-13 : 1108792510
Rating : 4/5 (16 Downloads)

Synopsis Facets of Algebraic Geometry by : Paolo Aluffi

Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry.

Contributions to Algebraic Geometry

Contributions to Algebraic Geometry
Author :
Publisher : European Mathematical Society
Total Pages : 520
Release :
ISBN-10 : 3037191147
ISBN-13 : 9783037191149
Rating : 4/5 (47 Downloads)

Synopsis Contributions to Algebraic Geometry by : Piotr Pragacz

The articles in this volume are the outcome of the Impanga Conference on Algebraic Geometry in 2010 at the Banach Center in Bedlewo. The following spectrum of topics is covered: K3 surfaces and Enriques surfaces Prym varieties and their moduli invariants of singularities in birational geometry differential forms on singular spaces Minimal Model Program linear systems toric varieties Seshadri and packing constants equivariant cohomology Thom polynomials arithmetic questions The main purpose of the volume is to give comprehensive introductions to the above topics, starting from an elementary level and ending with a discussion of current research. The first four topics are represented by the notes from the mini courses held during the conference. In the articles, the reader will find classical results and methods, as well as modern ones. This book is addressed to researchers and graduate students in algebraic geometry, singularity theory, and algebraic topology. Most of the material in this volume has not yet appeared in book form.

Bridging Algebra, Geometry, and Topology

Bridging Algebra, Geometry, and Topology
Author :
Publisher : Springer
Total Pages : 295
Release :
ISBN-10 : 9783319091860
ISBN-13 : 3319091867
Rating : 4/5 (60 Downloads)

Synopsis Bridging Algebra, Geometry, and Topology by : Denis Ibadula

Algebra, geometry and topology cover a variety of different, but intimately related research fields in modern mathematics. This book focuses on specific aspects of this interaction. The present volume contains refereed papers which were presented at the International Conference “Experimental and Theoretical Methods in Algebra, Geometry and Topology”, held in Eforie Nord (near Constanta), Romania, during 20-25 June 2013. The conference was devoted to the 60th anniversary of the distinguished Romanian mathematicians Alexandru Dimca and Ştefan Papadima. The selected papers consist of original research work and a survey paper. They are intended for a large audience, including researchers and graduate students interested in algebraic geometry, combinatorics, topology, hyperplane arrangements and commutative algebra. The papers are written by well-known experts from different fields of mathematics, affiliated to universities from all over the word, they cover a broad range of topics and explore the research frontiers of a wide variety of contemporary problems of modern mathematics.

Current Developments in Algebraic Geometry

Current Developments in Algebraic Geometry
Author :
Publisher : Cambridge University Press
Total Pages : 437
Release :
ISBN-10 : 9780521768252
ISBN-13 : 052176825X
Rating : 4/5 (52 Downloads)

Synopsis Current Developments in Algebraic Geometry by : Lucia Caporaso

This volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.

Interactions with Lattice Polytopes

Interactions with Lattice Polytopes
Author :
Publisher : Springer Nature
Total Pages : 368
Release :
ISBN-10 : 9783030983277
ISBN-13 : 3030983277
Rating : 4/5 (77 Downloads)

Synopsis Interactions with Lattice Polytopes by : Alexander M. Kasprzyk

This book collects together original research and survey articles highlighting the fertile interdisciplinary applications of convex lattice polytopes in modern mathematics. Covering a diverse range of topics, including algebraic geometry, mirror symmetry, symplectic geometry, discrete geometry, and algebraic combinatorics, the common theme is the study of lattice polytopes. These fascinating combinatorial objects are a cornerstone of toric geometry and continue to find rich and unforeseen applications throughout mathematics. The workshop Interactions with Lattice Polytopes assembled many top researchers at the Otto-von-Guericke-Universität Magdeburg in 2017 to discuss the role of lattice polytopes in their work, and many of their presented results are collected in this book. Intended to be accessible, these articles are suitable for researchers and graduate students interested in learning about some of the wide-ranging interactions of lattice polytopes in pure mathematics.

Numerically Solving Polynomial Systems with Bertini

Numerically Solving Polynomial Systems with Bertini
Author :
Publisher : SIAM
Total Pages : 372
Release :
ISBN-10 : 9781611972702
ISBN-13 : 1611972701
Rating : 4/5 (02 Downloads)

Synopsis Numerically Solving Polynomial Systems with Bertini by : Daniel J. Bates

This book is a guide to concepts and practice in numerical algebraic geometry ? the solution of systems of polynomial equations by numerical methods. Through numerous examples, the authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage options. The authors also maintain a complementary web page where readers can find supplementary materials and Bertini input files. Numerically Solving Polynomial Systems with Bertini approaches numerical algebraic geometry from a user's point of view with numerous examples of how Bertini is applicable to polynomial systems. It treats the fundamental task of solving a given polynomial system and describes the latest advances in the field, including algorithms for intersecting and projecting algebraic sets, methods for treating singular sets, the nascent field of real numerical algebraic geometry, and applications to large polynomial systems arising from differential equations. Those who wish to solve polynomial systems can start gently by finding isolated solutions to small systems, advance rapidly to using algorithms for finding positive-dimensional solution sets (curves, surfaces, etc.), and learn how to use parallel computers on large problems. These techniques are of interest to engineers and scientists in fields where polynomial equations arise, including robotics, control theory, economics, physics, numerical PDEs, and computational chemistry.

Commutative Algebra and Noncommutative Algebraic Geometry

Commutative Algebra and Noncommutative Algebraic Geometry
Author :
Publisher : Cambridge University Press
Total Pages : 463
Release :
ISBN-10 : 9781107065628
ISBN-13 : 1107065623
Rating : 4/5 (28 Downloads)

Synopsis Commutative Algebra and Noncommutative Algebraic Geometry by : David Eisenbud

This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 1 contains expository papers ideal for those entering the field.

Computer Algebra in Scientific Computing

Computer Algebra in Scientific Computing
Author :
Publisher : Springer
Total Pages : 525
Release :
ISBN-10 : 9783319456416
ISBN-13 : 3319456415
Rating : 4/5 (16 Downloads)

Synopsis Computer Algebra in Scientific Computing by : Vladimir P. Gerdt

This book constitutes the proceedings of the 18th International Workshop on Computer Algebra in Scientific Computing, CASC 2016, held in Bucharest, Romania, in September 2016. The 32 papers presented in this volume were carefully reviewed and selected from 39 submissions. They deal with cutting-edge research in all major disciplines of Computer Algebra.