報告題目：Spare Resultants for Differential and Difference Polynomial Equations

講座時間：2023年10月24日下午14:00--15:00

講座地點：騰訊會議 956180906

報告人：李偉

摘要：The (sparse) resultant gives conditions for an over-determined system of polynomial equations to have common solutions. As a basic concept in algebraic geometry, the (sparse) resultant also emerges to be one of the most powerful computational tools in (sparse) elimination theory due to its ability to eliminate several variables simultaneously. In the recent years, we developed theories of sparse differential resultants and sparse difference resultants, which extended the core theory of sparse resultants into algebraic differential and difference equations. Meanwhile, many new problems have arisen. In this talk, I will give an overview of the theory and algorithmic aspects of sparse differential resultants as well as sparse difference resultants, and present several open problems.

報告人簡介：李偉，中國科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院副研究員。本科畢業(yè)于山東大學(xué)，博士畢業(yè)于中科院數(shù)學(xué)與系統(tǒng)科學(xué)研究院，美國加州大學(xué)伯克利分校訪問學(xué)者。主持國家自然科學(xué)基金委優(yōu)秀青年基金；曾獲國際計算機協(xié)會(ACM) SIGSAM/ISSAC杰出論文獎、吳文俊計算機數(shù)學(xué)青年學(xué)者獎、中科院優(yōu)秀博士學(xué)位論文、入選中科院青年創(chuàng)新促進會、中科院數(shù)學(xué)院“陳景潤未來之星”等。研究方向為微分代數(shù)幾何、符號計算,主要成果包括：與合作者建立了微分周形式與微分周簇理論，發(fā)展了稀疏微分結(jié)式的理論及單指數(shù)消元算法，證明了微分-差分方程的有效Hilbert零點定理。成果主要發(fā)表在Found. Comput. Math., Trans. Amer. Math. Soc., J. London Math. Soc., J. Symb. Comput.等期刊。

主辦：研究生院

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