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A Course in Real Algebraic Geometry

- Positivity and Sums of Squares
Af: Claus Scheiderer Engelsk Hardback

A Course in Real Algebraic Geometry

- Positivity and Sums of Squares
Af: Claus Scheiderer Engelsk Hardback
Tjek vores konkurrenters priser

This textbook is designed for a one-year graduate course in real algebraic geometry, with a particular focus on positivity and sums of squares of polynomials.

The first half of the book features a thorough introduction to ordered fields and real closed fields, including the Tarski–Seidenberg projection theorem and transfer principle. Classical results such as Artin''s solution to Hilbert''s 17th problem and Hilbert''s theorems on sums of squares of polynomials are presented in detail. Other features include careful introductions to the real spectrum and to the geometry of semialgebraic sets. The second part studies Archimedean positivstellensätze in great detail and in various settings, together with important applications. The techniques and results presented here are fundamental to contemporary approaches to polynomial optimization. Important results on sums of squares on projective varieties are covered as well. The last part highlights applications to semidefinite programming and polynomial optimization, including recent research on semidefinite representation of convex sets.

Written by a leading expert and based on courses taught for several years, the book assumes familiarity with the basics of commutative algebra and algebraic varieties, as can be covered in a one-semester first course. Over 350 exercises, of all levels of difficulty, are included in the book.

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This textbook is designed for a one-year graduate course in real algebraic geometry, with a particular focus on positivity and sums of squares of polynomials.

The first half of the book features a thorough introduction to ordered fields and real closed fields, including the Tarski–Seidenberg projection theorem and transfer principle. Classical results such as Artin''s solution to Hilbert''s 17th problem and Hilbert''s theorems on sums of squares of polynomials are presented in detail. Other features include careful introductions to the real spectrum and to the geometry of semialgebraic sets. The second part studies Archimedean positivstellensätze in great detail and in various settings, together with important applications. The techniques and results presented here are fundamental to contemporary approaches to polynomial optimization. Important results on sums of squares on projective varieties are covered as well. The last part highlights applications to semidefinite programming and polynomial optimization, including recent research on semidefinite representation of convex sets.

Written by a leading expert and based on courses taught for several years, the book assumes familiarity with the basics of commutative algebra and algebraic varieties, as can be covered in a one-semester first course. Over 350 exercises, of all levels of difficulty, are included in the book.

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Produktdetaljer
Sprog: Engelsk
Sider: 404
ISBN-13: 9783031692123
Indbinding: Hardback
Udgave:
ISBN-10: 3031692128
Kategori: Algebraisk geometri
Udg. Dato: 13 sep 2024
Længde: 27mm
Bredde: 162mm
Højde: 241mm
Forlag: Springer International Publishing AG
Oplagsdato: 13 sep 2024
Forfatter(e): Claus Scheiderer
Forfatter(e) Claus Scheiderer

Kategori Algebraisk geometri

ISBN-13 9783031692123

Sprog Engelsk

Indbinding Hardback

Sider 404

Udgave

Længde 27mm

Bredde 162mm

Højde 241mm

Udg. Dato 13 sep 2024

Oplagsdato 13 sep 2024

Forlag Springer International Publishing AG