CAREER: Non-abelian Hodge Theory and Monodromy Actions

Katzarkov9875383该奖项资助研究和教育计划，特别强调代数几何和nonabelian霍奇理论。 研究者计划利用C。辛普森 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，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辅导，该倡议将这些学生带到校园进行辅导并帮助他们参加竞争性考试。 此外，调查员打算提高研究生和博士后研究员在欧文的机会，在代数geometrical.The国家科学基金会的研究讲习班组织强烈鼓励学术教师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）计划是一个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。 它在一个单一的计划中结合了最广泛意义上的高质量研究和教育的支持，以及那些传统上在科学和工程领域代表性不足的人的充分参与。 该计划增强并强调了基金会对全面，平衡的学术生涯发展的重要性。

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.