9500557 Maskit This project is concerned with several different aspects of complex analysis and function theory: moduli of Riemann surfaces via Eichler cohomology of Kleinian groups, the Schottky problem, geometric formulation of 2-dimensional quantum gravity, and Hausdorff dimension and the boundary behavior of conformal mappings are among the topics proposed. Function theory is the study of functions of one independent complex variable, and has a classical origin. A notable aspect of function theory is the use of Riemann surfaces; given a locally defined complex function one associates an abstract (multi-sheeted) surface, called the Riemann surface of the function, via analytic continuation. This Riemann surface carries all the essential information about the original function and its possible regular extensions. The proposed project has to do with classifying and understanding the totality of such Riemann surfaces.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
9500557
Program Officer
Christopher W. Stark
Project Start
Project End
Budget Start
1995-06-01
Budget End
1999-05-31
Support Year
Fiscal Year
1995
Total Cost
$405,000
Indirect Cost
Name
State University New York Stony Brook
Department
Type
DUNS #
City
Stony Brook
State
NY
Country
United States
Zip Code
11794