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数聚西海岸科学讲堂2024年第17期:Jingping Wang教授学术报告

发布时间:2024-04-23 阅读量:

报告题目:Hamiltonian, preHamiltonian and Nijenhuis rational difference operators

报告人: Jingping Wang

工作单位: University of Kent, UK

报告时间:4月26日(周五)15:00-16:00

地点:实训楼1710

报告摘要:

We introduce preHamiltonian pairs of difference operators and study their connections with Nijenhuis and Hamiltonian operators.
A difference operator is called preHamiltonian if its image is a Lie subalgebra with respect to the Lie bracket of evolutionary vector fields on a difference field. Two preHamiltonian operators form a preHamiltonian pair if any their linear combination is preHamiltonian. Then we show that preHamiltonian pairs naturally lead to Nijenhuis operators. Moreover, Nijenhuis operators can be represented in terms of a preHamiltonian pair. This provides a systematic method to check whether a rational operator is Nijenhuis.
We explore the link between preHamiltonian and Hamiltonian operators and show show that if H is a rational Hamiltonian operator, then to find a second Hamiltonian operator K compatible with H is the same as to find a preHamiltonian pair A and B such that K=AB^{-1}H is skew-symmetric.
In the end, we illustrate our theory on known and new examples. This is the joint work with S. Carpentier and A.V. Mikhailov.

报告人简介:

Jingping Wang, 本科毕业于北京大学,博士毕业于荷兰鹿特丹大学, 现为英国肯特大学教授、博士生导师, 主要从事可积系统理论的研究工作, 在Commun. Math. Phys., Lett. Math. Phys.等期刊上发表多篇高质量SCI论文。