CAREER: Non-abelian Hodge Theory and Monodromy Actions

职业：非阿贝尔霍奇理论和单峰行为

• 批准号: 9875383
• 负责人: Ludmil Katzarkov
• 金额: $ 20万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-10-01 至 2004-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9875383&HistoricalAwards=false
• 关键词: CAREER; Non; abelian; Hodge; Theory

Katzarkov9875383This award funds programs for research and education with special emphasis in algebraic geometry and nonabelian Hodge theory. The investigator plans to study the actions of homotopy groups and homology groups on homotopy types of varieties using developments in nonabelian Hodge theory as introduced by C. Simpson. The investigator hopes to shed light on the interplay between the geometric structure of algebraic varieties and the representation theory of their fundamental groups. In addition to his research, the investigator proposes a number of broadly based activities for the promotion of education at all levels. This includes the mentoring of high school students through the Mathematical Circles initiative, which brings these students to campus for tutoring and help in competitive exams. Moreover, the investigator intends to enhance opportunities for graduate students and postdoctural fellows at Irvine by organization of research workshops in algebraic geometry.The National Science Foundation strongly encourages the early development of academic faculty as both educators and researchers. The Faculty Early Career Development (CAREER) Program is a Foundation-wide program that provides for the support of junior faculty within the context of their overall career development. It combines in a single program the support of quality research and education in the broadest sense and the full participation of those traditionally underrepresented in sciences and engineering. This program enhances and emphasizes the importance the Foundation places on the development of full, balanced academic careers.

Katzarkov9875383该奖项资助研究和教育项目，特别强调代数几何和非阿贝尔霍奇理论。 研究人员计划利用 C. Simpson 介绍的非阿贝尔霍奇理论的发展来研究同伦群和同伦群对品种同伦类型的作用。 研究人员希望阐明代数簇的几何结构与其基本群的表示论之间的相互作用。 除了他的研究之外，研究者还提出了一些基础广泛的活动来促进各级教育。 这包括通过数学圈计划对高中生进行指导，该计划将这些学生带到校园接受辅导并帮助他们参加竞争性考试。 此外，研究人员打算通过组织代数几何研究研讨会来增加欧文分校研究生和博士后的机会。国家科学基金会大力鼓励学术人员作为教育工作者和研究人员的早期发展。 教师早期职业发展（CAREER）计划是一项基金会范围内的计划，为初级教师的整体职业发展提供支持。 它将最广泛意义上的高质量研究和教育的支持以及传统上在科学和工程领域代表性不足的人们的充分参与结合在一个计划中。 该计划增强并强调了基金会对全面、平衡的学术职业发展的重视。