Book Review: Real solutions to equations from geometry

DOI10.1090/S0273-0979-2013-01397-1zbMath1272.00022OpenAlexW2321286172MaRDI QIDQ2849020

Michael Shapiro

Publication date: 16 September 2013

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-2013-01397-1

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Grassmannians, Schubert varieties, flag manifolds (14M15) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Topology of real algebraic varieties (14P25) Classical problems, Schubert calculus (14N15) External book reviews (00A17) Real algebraic and real-analytic geometry (14Pxx)

Cites Work

• The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz
• All knots are algebraic
• The topology of real algebraic sets with isolated singularities
• On bounding the Betti numbers and computing the Euler characteristic of semi-algebraic sets
• Rational functions with real critical points and the B. and M. Shapiro conjecture in real enumerative geometry
• Blowup equivalence of smooth closed manifolds
• Invariants of real symplectic 4-manifolds and lower bounds in real enumerative geometry
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Real algebraic manifolds
• Submanifolds and Homology of Nonsingular Real Algebraic Varieties
• The Nash conjecture for threefolds
• Mystery of point charges
• The Historical Development of Algebraic Geometry
• On the Betti Numbers of Real Varieties
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