Distance geometry, algebra and drones

• Gregor Kemper ^[1]
  1. [1] Technical University Munich

     Technical University Munich

     Kreisfreie Stadt München, Alemania

     
• Localización: EACA 2022: XVII Encuentro de Álgebra Computacional y Aplicaciones / coord. por Carlos Galindo Pastor, Philippe Giménez, Fernando Javier Hernando Carrillo, F. Monserrat Delpalillo, Julio José Moyano Fernández, 2023, ISBN 978-84-19647-46-7, pág. 19
• Idioma: inglés
• Enlaces
  • Texto Completo Libro
• Resumen

  • Is it always possible to reconstruct a point configuration in the plane from the unlabeled set of mutual distances between the points? This and other questions translate to invariant theory and ultimately into problems about polynomial ideals. As it turns out, the following question is related: can a drone detect the walls of a room from hearing the echoes of a sound? What if the time at which the sound was emitted is unknown? Attacking these questions again leads to ideal theory and requires massive computer algebra computations. The talk presents results by Mireille Boutin and the speaker, some of which are old and some very recent.