seminar: Does there exist quadratic relations among logarithms of algebraic numbers?

speaker: Michel Waldschmidt (Faculté de Mathématiques, Université Pierre et Marie Curie)

abstract: The answer to the title question is conjecturally "no, apart from trivial ones". We give a survey on the state of the art on this topic: very few results are known, they deal with homogeneous relations. We add the following item to the very limited collection of answers to this question, dealing with non homogeneous relations.

The Strong Six Exponentials Theorem of D.~Roy deals with $2\times 3$ matrices whose entries are linear combinations, with algebraic coefficients, of $1$ and logarithms of algebraic numbers. Under suitable assumptions, such a matrix has rank $2$. Here we investigate the three $2\times 2$ determinants: under suitable assumptions, one at least is not a linear combination, with algebraic coefficients, of $1$ and logarithms of algebraic numbers.

timetable:
Thu 26 May, 10:00 - 11:00, Sala Conferenze Centro De Giorgi
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