000			02491nam a22003377a 4500
003			IIITD
005			20250521171704.0
008			250514b |||||||| |||| 00| 0 eng d
020			_a9783031692123
040			_aIIITD
082			_a516.35 _bSCH-C
100			_aScheiderer, Claus
245			_aA course in real algebraic geometry : _bpositivity and sums of squares _cby Claus Scheiderer
260			_aSwitzerland : _bSpringer, _c©2024
300			_axviii, 404 p. : _bill. ; _c24 cm.
490			_aGraduate Texts in Mathematics
504			_aIncludes bibliographical references and index
505			_t1. Ordered fields
505			_t2. Positive polynomials and sums of squares
505			_t3. The real spectrum
505			_t4. Semialgebraic geometry
505			_t5. The archimedean property
505			_t6. Positive polynomials with zeros
505			_t7. Sums of squares on projective varities
505			_t8. Sums of squares and optimization
520			_aThis 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. Collapse summary
650			_aMathematics
650			_aAlgebra
650			_aGeometry
942			_cBK _2ddc
999			_c189952 _d189952