Quantitative geometry

Quantitative geometry.

Rather than describing a traditional field of mathematics, “quantitative geometry” refers to a modern way of thinking about geometry and its applications that occur in a wide range of mathematical disciplines. The overarching theme here is that certain geometric problems can only be formulated after the introduction of auxiliary quantitative parameters and asking for their asymptotic or approxi...

Quantitative symplectic geometry

Symplectic capacities were introduced in 1990 by I. Ekeland and H. Hofer [19, 20] (although the first capacity was in fact constructed by M. Gromov [40]). Since then, lots of new capacities have been defined [16, 30, 32, 44, 49, 59, 60, 90, 99] and they were further studied in [1, 2, 8, 9, 17, 26, 21, 28, 31, 35, 37, 38, 41, 42, 43, 46, 48, 50, 52, 56, 57, 58, 61, 62, 63, 64, 65, 66, 68, 74, 75...

Quantitative Combinatorial Geometry for Continuous Parameters

38 COMPUTATIONAL and QUANTITATIVE REAL ALGEBRAIC GEOMETRY

Computational and quantitative real algebraic geometry studies various algorithmic and quantitative questions dealing with the real solutions of a system of equalities, inequalities, and inequations of polynomials over the real numbers. This emerging field is largely motivated by the power and elegance with which it solves a broad and general class of problems arising in robotics, vision, compu...

37 Computational and Quantitative Real Algebraic Geometry

Computational and quantitative real algebraic geometry studies various algorithmic and quantitative questions dealing with the real solutions of a system of equalities, inequalities, and inequations of polynomials over the real numbers. This emerging field is largely motivated by the power and elegance with which it solves a broad and general class of problems arising in robotics, vision, compu...