Combinatorical and Algebraic Structures Seminar

Session details

Date: 19.3.2019
Speaker: Hana Dlouhá, FJFI, České vysoké učení technické v Praze
Title: Algebraic properties of multidimensional continued fractions
Abstract: In 1839 Hermite posed to Jacobi the problem of finding a method for representing real numbers by sequences of non-negative integers, such that the periodic representations would correspond to the algebraic properties of the numbers (especially to the degree). Continued fractions completely solve this problem for quadratic irrationalities, but for numbers of degree $\geq 3$ it showed to be a very hard problem. Starting with Jacobi, there were published many modifications of the classical continued fraction algorithm, called multidimensional continued fractions, that attempts to solve this question. In this talk we give a summary of the vectorial multidimensional continued fractions and its algebraic properties.

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