CAREER: Renormalization and higher rank parabolic actions

职业生涯：重整化和更高阶的抛物线作用

• 批准号: 2143133
• 负责人: Rodrigo Trevino
• 金额: $ 50万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-06-01 至 2027-05-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2143133&HistoricalAwards=false
• 关键词: CAREER; Renormalization; higher; rank; parabolic

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). This project aims to advance knowledge on parabolic systems, which refer to a class of complex systems that appear in many areas of mathematics as well as physics. There is a significant educational component: this project plans to support the activities of the Laboratory of Experimental Mathematics, of which the PI is a co-director, as well as the Girls Talk Math (GTM) program, both hosted at the University of Maryland. The former activity is aimed at engaging undergraduate students in research, and the latter at attracting high-school students from underrepresented groups towards the STEM-disciplines.Parabolic systems are the types of dynamical systems that are neither chaotic (that is, exhibit exponential complexity), nor completely rigid. Parabolic systems typically exhibit a type of polynomial complexity. An example of one such system is the motion of a particle on a frictionless and pocketless billiard table of non-rectangular polygonal shape with completely elastic collisions at the boundary. Higher rank parabolic systems appear in the study of aperiodic tilings, closely connected to applications to mathematical physics. Parabolic systems can be studied through techniques known as renormalization methods. A significant component of the project is devoted to developing renormalization tools in the language of operator algebras, that is, using invariants coming from operator algebras to obtain dynamical invariants.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项全部或部分由《2021年美国救援计划法案》（公法117-2）资助。该项目旨在推进抛物系统的知识，抛物系统指的是一类复杂系统，出现在数学和物理的许多领域。有一个重要的教育组成部分：该项目计划支持实验数学实验室的活动，PI是其中的联合主任，以及女孩谈论数学（GTM）计划，两者都在马里兰大学主持。前一项活动旨在吸引本科生参与研究，后一项活动旨在吸引来自代表性不足群体的高中生进入stem学科。抛物系统是一种既不是混沌的（即表现出指数复杂性），也不是完全刚性的动力系统。抛物型系统通常表现出一种多项式复杂度。一个这样的系统的例子是一个粒子在一个无摩擦和无口袋的非矩形多边形台球桌上的运动，在边界有完全弹性碰撞。高阶抛物系统出现在非周期平铺的研究中，与数学物理的应用密切相关。抛物系统可以通过称为重整化方法的技术来研究。该项目的一个重要组成部分是致力于开发算子代数语言中的重整化工具，即使用来自算子代数的不变量来获得动态不变量。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。