｜事業推進担当者｜COE研究員｜COE事務室｜ 教官氏名 VIDUNAS, Raimundas 所属部局名、 学科部門名 数理学研究院 職名 ＣＯＥ博士研究員 電子メール vidunas@math.kyushu-u.ac.jp ホームページ http://www.math.kyushu-u.ac.jp/~vidunas 電話番号 092-642-7047 FAX番号 092-642-7047 取得学位 PhD in Mathematics and Natural Sciences・ Groningen University (The Netherlands)・ October 1999 専門分野 Hypergeometric functions・Non-commutative geometry・Splines 研究・教育・ 社会活動概要 The theme of my Phd thesis is computer algebra of differential equations and splines. I characterized second order linear homogeneous differential equations with certain differential Galois groups, and computed spaces of two-dimensional splines. My first post-doc project (1999-2001) was "Algorithmic Methods for Special Functions by Computer Algebra". My aim was to generalize Zeilberger-type algorithms to the case of nonterminating hypergeometric series, and to develop computer algebra methods for uniform asymptotics theory for special fucntions. My second post-doc project (2002-2003) was a study of non-commutative geometry and representation theory. Currently I am most active within the special functions community. I am developing my earlier work on classification of hypergeometric identities, and I am interested in applications of special functions to non-commutative geometry. 研究のキーワード Hypergeometric functions, orthogonal polynomials, Zeilberger's algorithm, non-commutative geometry, quantum groups, Leonard pairs, splines. 研究業績 [1]　 R. Vidunas, "Transformations of some Gauss hypergeometric functions", submitted to the "Journal of Computational and Applied Mathematics", for the proceedings of OPSFA 7 symposium (August 2003, Copenhagen). Available at http://arXiv.org/abs/math.CA/0310436. [2]　 P. Terwilliger, R. Vidunas, "Leonard pairs and the Askey-Wilson relations", submitted to "Journal of Algebra and its Applications", available at http://arXiv.org/abs/math.QA/0305356. [3]　 R. Vidunas, "Contiguous relations of hypergeometric functions", in "Journal of Computational and Applied Mathematics", Vol. 153 (2003), pg. 507--519. [4]　 R. Vidunas, "A generalization of Kummer's identity", in "Rocky Mountain Journal of Mathematics", Vol. 32, No. 2 (2002), pg. 919--936. [5]　 R. Vidunas, "Geometrically continuous octahedron", accepted for the proceedings of the workshop on Algebraic Geometry and Geometric Modelling (AGGM2002) in Vilnius, Lithuania, July 29--August 2, 2002. To appear in the AMS series ``Contemporary Mathematics". [6]　 N.M. Temme, R. Vidunas, "Parabolic cylinder functions: error bounds for asymptotic expansions", in "Analysis and applications", Vol. 1, No 3 (2003), pg. 265-288. [7]　 R. Vidunas, N.M. Temme, "Symbolic evaluation of coefficients in Airy-type asymptotic expansions", in "Journal of Mathematical Analysis and Applications'', Vol. 269 (2002), pg. 317--331. [8]　 F. Beukers, R. van Luijk, R. Vidunas, "A linear algebra exercise", in ``Nieuw Archief voor Wiskunde" (a journal of the Dutch Mathematical Society), Series V, Vol. 3, No. 2 (2002), pg. 42--43. [9]　 R. Vidunas, "Differential equations of order two with one singular point", in "Journal of Symbolic Computation'', Vol. 28, No. 4--5 (1999), pg. 495--520. 所属学会名 The Royal Dutch Mathematical Society (from 2001), The American Mathematical Society (1994). 教育活動 I taught various classes on computer algebra, algorithm theory, functional analysis, linear algebra, special functions at Groningen University and at University of Amsterdam. 社会連携活動 A presentation "Approaching the Rainbow", given at the CWI buisiness day(October 2001, Amsterdam). AMS reviewer その他 - ｜事業推進担当者｜COE研究員｜COE事務室｜