CAREER: Non-abelian Hodge Theory and Monodromy Actions

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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.