Quasiconformal Geometry and Elliptic PDEs
Month: May 2013
Date: May 20--24
Name: Quasiconformal Geometry and Elliptic PDEs
Location: Institute for Pure and Applied Mathematics (IPAM), UCLA, Los Angeles, California.
The theories of quasiconformal mappings and elliptic partial differential equations have classical connections dating back the work of Vekua, Bers, Bojarski, and others. During the last ten years these connections have been revitalized through new methods and breakthroughs and surprising applications that merge geometric and analytic methods. These include the solution of Calderon's problem of impedance tomography in the plane by Astala and Paivarinta.$\;$ Current research suggests that the methods of geometric analysis will also be applicable to problems in materials sciences, such as in elasticity and stochastic homogenization. Another development is the extension of the theory to degenerate elliptic equations, through the work of David, Iwaniec, Koskela, Martin and many others. Here the geometric counterpart is the theory of mappings of finite distortion, which played a vital role in recent work on random geometry. The workshop will also study the conformal geometry related open problem.