Mathematical Sciences: The Markoff Spectrum and Higher Dimensional Approximation Constants/Conference at BYU; May 20-26, 1991

A. A. Markoff在1872年描述了 关于可逼近性差的真实的数的可逼近性， 二次型及其齐次最小值的序列。 的 研究这个-第一个马尔可夫链-和相应的 其他真实的数字和形式的理论已经取得了相当大的进展， 过去二十年的进步。 一个方向是 研究光谱本身的结构 第二个方向是 增加了对双曲型 上的自由群的几何及其与代数的联系 两台发电机 许多详细的技术计算都依赖于 关于测地线的切割序列， 研究中出现的所谓双距离序列， 准晶体 这笔赠款将部分支持为期六天的研讨会， 马尔可夫谱和高维近似常数 1991年5月在杨百翰大学举行。 讲习班 将促进信息交流，并鼓励 大约30名数学家在几个相关领域进行了研究， 与丢番图近似有关的数学领域。 这一领域最近取得的成果使举办这样一个讲习班非常及时。

The seminal work of A.A. Markoff in 1872 described the degree of approximability of badly approximable real numbers in terms of a sequence of quadratic forms and their homogeneous minima. The study of this - the first Markoff Chain - and of the corresponding theory for other real numbers and forms has made considerable progress over the last twenty years. One direction has been to study the structure of the spectrum itself. A second direction has been to increase the understanding of the relevance of hyperbolic geometry and the connection with the algebra of the free group on two generators. Much of the detailed technical calculations rely on the cutting sequences of the geodesics which in turn are related to the so-called two-distance sequences arising in the study of quasi-crystals. This grant will partially support a six day workshop on the Markoff spectrum and higher dimensional approximation constants to be held at Brigham Young University in May, 1991. The workshop will facilitate the exchange of information and will encourage the research of about thirty mathematicians working in several related areas of mathematics connected with Diophantine Approximation. Recent results in this area make such a workshop most timely.