北航数学论坛学术报告

Effective Nullstellensatz for Algebraic Differential-Difference Equations

李伟 副研究员

(中国科学院数学与系统科学研究院)

时间：2023年11月13日（周一下午）4:30-5:30

地点：北京航空航天大学沙河校区J3-101

摘要：

Hilbert’s Nullstellensatz is a cornerstone in algebraic geometry. Its effective version, known as the effective Nullstellensatz, provides an algorithm for consistency checking of polynomial equations. Algebraic differential-difference equations, or what are called algebraic delay differential equations, are ubiquitous in applications, and consistency checking is a basic problem in solving delay differential equations, which seeks for a general method or algorithm to determine whether an arbitrarily given system of delay differential equations has a sequence solution.

  We solve this problem positively by proving the effective (partial) differential-difference Hilbert’s Nullstellensatz theorem, in which we derive an explicit upper bound for the number of iterated applications of the distinguished difference and derivation operators, for a reduction of this differential-difference consistency-checking problem to a well-studied consistency-checking problem for polynomial equations. In this talk, we will first give a brief introduction to the effective Hilbert’s Nullstellensatz in algebraic geometry. Then we discuss our results on effective Nullstellensatz and consistency-checking problems for delay differential equations, and also for delay PDEs. This is joint work with A. Ovchinnikov, G. Pogudin and T. Scanlon.

报告人简介:

李伟，中国科学院数学与系统科学研究院副研究员。本科毕业于山东大学，博士毕业于中科院数学与系统科学研究院。主持国家自然科学基金委国家级青年基金；曾获国际计算机协会(ACM) SIGSAM/ISSAC杰出论文奖、吴文俊计算机数学青年学者奖、中科院优秀博士学位论文、入选中科院数学院“陈景润未来之星”、中科院青年创新促进会等。主要研究方向为微分代数几何、符号计算。

邀请人：唐晓弦

欢迎大家参加！