Talk
Exact Computations with Integrals of Univariate Algebraic Functions
- Emre Sertöz (Leiden University)
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).