Diophantine Approximation for systems of linear forms - some comments on inhomogeneity, monotonicity, and primitivity

Abstract: Diophantine Approximation is a branch of Number Theory in which the central theme is understanding how well real numbers can be approximated by rationals. In the most classical setting, a $\psi$-well-approximable number is one which can be approximated by rationals to a given degree of accuracy specified by an approximating function $\psi$. Khintchine's Theorem provides a beautiful characterisation of the Lebesgue measure of the set of $\psi$-well-approximable numbers and is one of the cornerstone results of Diophantine Approximation. In this talk I will discuss the generalisation of Khintchine's Theorem to the setting of approximation for systems of linear forms. I will focus mainly on the topic of inhomogeneous approximation for systems of linear forms. Time permitting, I may also discuss approximation for systems of linear forms subject to certain primitivity constraints. This talk will be based on joint work with Felipe Ramirez (Wesleyan, US).

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )

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One World Numeration seminar

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