These proceedings from the 2004 conference describe significant advances in differential and algebraic geometry and their connections to number theory and mathematical physics. Topics include optimal control of the Lieuville equation, real structures on torus bundles and their deformations, , representations of finite Lie algebras and geometry of reductive lie algebras, multi-parameter cells of finite Coxeter groups, rigidity problems in Cauchy-Riemann analysis, periods of automorphic forms, problems with Hamiltonian line graphs, localization and string quality, the second main theorem with hypersurfaces over function fields, presentations for finite complex reduction groups, perspectives on geometric analysis, automorphisms of K3 surfaces and vector bundles on certain surfaces without divisors. Annotation ©2007 Book News, Inc., Portland, OR (booknews.com)