Prof. Dr. Takao Watanabe
Department of Mathematics, Graduate School of Science, Osaka University
Toyonaka, Osaka 560-0043, Japan
Office: B546, Building "B" of Graduate School of Science
Fax: +81-6-6850-5327

研究紹介 (Research Interests)

代数体上定義された代数的等質空間上の整数点あるいは有理点の height と旗多様体の一般Hermite定数 を研究しています. 2次形式の代数的理論, 格子の簡約理論, 代数体のイデアル格子にも興味を持っています. 最近の研究では, Ryshkov polyhedra を簡約可能線形代数群の height から定義される算術的最少関数に拡張し, それを用いてアデール算術商の基本領域を記述しました.

I study heights of rational points on algebraic homogeneous spaces defined over an algebraic number field and generalized Hermite's constants of flag varieties. I am interested in algebraic theory of quadratic forms, reduction theory of lattices, and ideal lattices of algebraic number fields. My recent work is a generalization of Ryshkov polyhedra to arithmetical minimum functions defined from height funcdions on reductive algebraic groups. By using this idea, I constructed fundamental domains for arithmetic quotients of adele groups.