[geometry-ml:05722] 東大数理・複素解析幾何セミナー 6/10

[shigeharu takayama]

皆様、

東大数理・複素解析幾何セミナーのお知らせです。

2024年06月10日(月)10:30-12:00
数理科学研究科棟(駒場) 128号室
講演者：鍋島 克輔 氏 (東京理科大学)
講演題目：Computing Noetherian operators of polynomial ideals
--How to characterize a polynomial ideal by partial differential
operators -- (Japanese)
[ 講演概要 ]
Describing ideals in polynomial rings by using systems of differential
operators in one of the major approaches to study them. In 1916, F.S.
Macaulay brought the notion of an inverse system, a system of
differential conditions that describes an ideal. In 1937, W. Groebner
mentioned the importance of the Macaulay's inverse system in the study
of linear differential equations with constant coefficient, and in
1938, he introduced differential operators to characterize ideals that
are primary to a rational maximal ideal. After that the important
results and the terminology came from L. Ehrenpreise and V. P.
Palamodov in 1961 and 1970, that is the characterization of primary
ideals by the differential operators. The differential operators allow
one to characterize the primary ideal by differential conditions on
the associated characteristic variety. The differential operators are
called Noetherian operators.
In this talk, we consider Noetherian operators in the context of
symbolic computation. Upon utilizing the theory of holonomic
D-modules, we present a new computational method of Noetherian
operators associated to a polynomial ideal. The computational method
that consists mainly of linear algebra techniques is given for
computing them. Moreover, as applications, new computational methods
of polynomial ideals are discussed by utilizing the Noetherian
operators.

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今後の予定はこちら
https://www.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

世話人
高山 茂晴、平地 健吾