We prove that there is no hope of trying to invent pseudoholomorphic theories of anything other than curves, even if one allows more general objects than almost complex manifolds. The hard part is dispensing with theories of pseudoholomorphic hypersurfaces; hypersurface theories exist “microlocally” (in abundance) but not “locally.”

Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their d...

Deep connections between complex numbers and geometry had been well known and carefully studied centuries ago. Fundamental objects that are investigated are the complex plane (usually extended by a single infinite point), its objects (points, lines and circles), and groups of transformations that act on them (e.g., inversions and Möbius transformations). In this paper we treat the geometry of c...

Generalized complex geometry encompasses complex and symplectic geometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group, elliptic deformation theory, relation to Poisson geometry, and local structure theory. We also define and study generalized complex branes, which interpolate between flat bundles on Lagrangian submanifold...

An efficient finite volume approach has been used to develop a three dimensional Helmholtz acoustic solver for complex geometries. This acoustic solver was utilized to obtain characteristic mode shapes and frequencies of a baffled combustion chamber. An experimental setup, including stationary and moving sensors, has also been used to measure these quantities for the same model combustion chamb...