Prof. Yves Andre:
From the impossibility of computing algebraically the position of a planet at prescribed time (Newton) to the general structure of period relations (Ayoub)
Zeit und Ort
Donnerstag, 28.4.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Zusammenfassung
\nAbstract: In lemma XXVIII of his Principia (1687), Newton asserts the\nimpossibility of computing algebraically the area of a section of a\nfixed oval in terms of the position of the line which cuts it. While the\nvalidity of both the statement and its proof have been vigorously\ndebated during three centuries, this has launched a vast reflection\nabout the transcendence of volumes of algebraic solids (as functions of\ndefining parameters), and more generally about the nature of the\nalgebraic relations relating such volumes. A general structure theorem,\nas simple to state as difficult to prove, has finally been found by J.\nAyoub (2015).\nIn this talk, we will review Newton’s lemma and its marvelous proof,\nstate the transcendence problem and explain Ayoub’s result.\n