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Exact Computations with Integrals of Univariate Algebraic Functions

  • Emre Sertöz (Leiden University)
G3 10 (Lecture hall)

Abstract

While it is impossible to construct an algorithm (Turing machine) capable of computing with arbitrary real numbers, many numbers of interest have a geometric origin, such as π, which reveals deep connections to polynomial algebra. For values arising in higher-dimensional geometry, the question of whether an algorithm can determine the equality of two given numbers remains unresolved. In this work, we address this question for areas of semi-algebraic shapes in the plane, using recent techniques from the theory of algebraic curves. This is joint work with Joël Ouaknine (MPI SWS) and James Worrell (Oxford).