CAREER: Geometric Function Theory in Several Complex Variables

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This CAREER award will support the PI's investigations of various geometric and analytic problems in several complex variables and Cauchy-Riemann geometry. The objective of the research is to further the present understanding of geometric function theory in several complex variables, as well as its connections with aspects of algebraic geometry, complex geometry, dynamical systems and physics. The project will develop new methods and provide interesting research topics for graduate students and postdocs. The PI will organize a series of educational activities for students of different academic levels, as well as secondary school educators. This includes a reading and research program for high school students, a learning and teaching program for high school teachers, and an undergraduate summer school program. The PI will encourage the participation of people from underrepresented groups and underserved school districts into these activities. The programs will also provide pedagogical training opportunities for graduate students. The Bergman kernel and metric will play a prominent role in the research. In particular, the geometry of open complex spaces will be investigated in terms of their Bergman kernels and metrics. The PI will also conduct research on the regularity and rigidity problems of Cauchy-Riemann and holomorphic mappings that naturally arise in several complex variables, complex geometry, and arithmetical algebraic geometry. The methods in the research will incorporate techniques from partial differential equations, algebra, and differential geometry, in addition to complex analysis.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.