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
Email: twatanabe＠math.sci.osaka-u.ac.jp
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. 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. また最近では, 大中鈴絵氏との研究でBugeaud氏とDong Han Kim氏により 導入されたスツルム語のある指数についての空隙の範囲を決定しました.
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 defined 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. Recently, Ms. Ohnaka and I determined a gap of some exponents of Sturmian words introduced by Professor Bugeaud and Professor Dong Han Kim.
・Lecture notes entitled "Reduction Theory of Arithmetic Quotients of Reductive Algebraic Groups" have been added in the "documents" folder .
・Professor Ichiro Satake's handwritten lecture notes have been added in the "documents" folder .