CAREER: Non-abelian Hodge Theory and Monodromy Actions

Katzarkov9875383该奖项为研究和教育项目提供资金，特别强调代数几何和非阿贝尔霍奇理论。研究者计划利用C.Simpson介绍的非交换Hodge理论的发展来研究同伦群和同调群对同伦类型的变种的作用。研究者希望阐明代数簇的几何结构与其基本群的表示理论之间的相互作用。除了他的研究之外，这位调查员还提出了一些基础广泛的活动，以促进各级教育。这包括通过数学圈倡议对高中生进行指导，该倡议将这些学生带到校园进行辅导，并在竞争性考试中提供帮助。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大学研究生和博士后研究员的机会。国家科学基金会大力鼓励学术人员早期发展为教育工作者和研究人员。学院早期职业发展(Career)计划是一个基础范围的计划，为初级教师在其整体职业发展的背景下提供支持。它在一个单一的计划中结合了对最广泛意义上的高质量研究和教育的支持，以及那些在科学和工程领域传统上代表性较低的人的充分参与。这一计划加强并强调了基金会对充分、平衡的学术事业发展的重要性。

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.