On the problem of emergence arising in hydrodynamic systems of collective behavior
数学专题报告
报告题目(Title)：On the problem of emergence arising in hydrodynamic systems of collective behavior
报告人(Speaker)：Roman Shvydkoy 教授 (University of Illinois at Chicago, USA)
地点(Place)：Zoom ID：825 444 64979, Passcode：123456, Zoom Link: https://us02web.zoom.us/j/82544464979
时间(Time)：2022 年 12 月 08 日(周四), 10:30-11:30
邀请人(Inviter)：薛留堂
报告摘要
Emergence is a phenomenon of formation of collective outcomes in systems where communications between agents has local range. In dynamics of swarms such outcomes often represent a globally aligned flock or congregation of aligned clusters. The classical result of Cucker and Smale states that alignment is unconditional in flocks that have global communication with non-integrable radial tails. Proving a similar statement for purely local interactions presents a major mathematical challenge. In this talk we will overview three programs of research directed on understanding the emergent phenomena: hydrodynamic topological interactions, kinetic approach based on hypocoercivity, and spectral energy method. We present a novel framework based on the concept of environmental averaging which allows us to obtain coercivity estimates leading to new flocking results.
主讲人简介
Roman Shvydkoy, 现为美国伊利诺伊大学芝加哥分校的教授. 目前已经在JAMS, ARMA, CMP, Adv. Math.等重要国际学术期刊上发表70余篇学术文章.
