Khintchine’s theorem on Diophantine approximation

Khintchine’s theorem on Diophantine approximation

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강연자 김성민
소속 서울대학교

Diophantine approximation is the study of approximating real numbers by rational numbers. For example, one can ask whether a real number x is ψ-approximable; that is, whether there are infinitely many rationals p/q satisfying |x-p/q|<ψ(q)/q for a given monotonic function ψ. A century ago, Khintchine discovered a remarkable dichotomy for the Lebesgue measure of the set of ψ-approximable numbers. Since then, Khintchine’s theorem has been extended in various directions, including inhomogeneous approximation and higher-dimensional generalizations. In this talk, I will introduce the Allen-Ramírez conjecture on removing the monotonicity condition from the inhomogeneous Khintchine-Groshev theorem and discuss a recent proof of the conjecture in the case (n,m)=(2,1).

음향문제로 강연 후반 음성이 출력되지 않습니다

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Now

현재 Khintchine’s theorem on Diophantine approximation

강연자 : 김성민 | 소속 : 서울대학교

Diophantine approximation is the study of approximating real numbers by rational numbers. For example, one can ask whether a real number x is ψ-approximable; that is, whether there are infinitely many rationals p/q satisfying |x-p/q|<ψ(q)/q for a given monotonic function ψ. A century ago, Khintchine discovered a remarkable dichotomy for the Lebesgue measure of the set of ψ-approximable numbers. Since then, Khintchine’s theorem has been extended in various directions, including inhomogeneous approximation and higher-dimensional generalizations. In this talk, I will introduce the Allen-Ramírez conjecture on removing the monotonicity condition from the inhomogeneous Khintchine-Groshev theorem and discuss a recent proof of the conjecture in the case (n,m)=(2,1).

음향문제로 강연 후반 음성이 출력되지 않습니다

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An algebraic function field is an algebraic extension of finite degree over the rational function field. This field was first introduced by Dedekind, Kronecker, and Weber in the nineteenth century and was further developed by Artin, Hasse, Schmidt, and Weil in the first half of the twentieth century. In this talk, we discuss various function field extensions over a finite field and examine important invariants such as the number of rational places and the class numbers.

음향문제로 강연 시작 4분 후부터 음성이 출력됩니다.

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