THE UNIVERSITY OF SOUTH DAKOTA
The Cauchy-Riemann complex is a system of partial differential equations describing the behavior of holomorphic functions, which are fundamental objects of study in many areas of pure and applied mathematics. The PI will investigate the properties of various solution operators on non-smooth domains (i.e. domains with corners) with relevance to problems in complex geometry, partial differential equations, and theoretical physics. In particular, the PI will investigate the extent to which the solution operators preserve smoothness of the given data, which has significant implications for the study of boundary values of holomorphic functions. As a special case, the PI will study situations where the solution operator is compact, which has applications in the study of Schrödinger operators and Toeplitz operators in mathematical physics. In addition to summer support, funding is requested primarily to facilitate collaboration with researchers at other universities and dissemination of results via support for off-campus travel.