We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conver...

The paper contains some new results and a review of recent achievements, concerning the multisupport solutions to matrix models. In the leading order of the ’t Hooft expansion for matrix integral, these solutions are described by quasiclassical or generalized Whitham hierarchies and are directly related to the superpotentials of four-dimensional N = 1 SUSY gauge theories. We study the derivativ...

A complex hyperbolic orbifold M can be written as HC/Γ where Γ is a discrete, faithful representation of π1(M) to Isom(H 2 C). The group SU(2, 1) is a triple cover of the group of holomorphic isometries of HC and (taking subgroups if necessary) we view Γ as a subgroup of SU(2, 1). Our main goal is to discuss the connection between the geometry of M and traces of Γ. We do this in two specific ca...

The theme of these four lectures is roughly "the history of, and some recent developments in, the study of algebraic geometry by analytic methods". Since this topic is much too broad I have chosen to isolate one particular analytic tool, the local notion of residue and subsequent global residue theorem, and will attempt to illustrate some ways in which residues may be used in both classical and...

In the first part of my talk, we consider special metrics on holomorphic bundles. We will recall the classical Hitchin-Kobayashi correspondence (Donaldson-Uhlenbeck-Yau theory) of stability and HermitianEinstein metrics on holomorphic vector bundles; and some generalizations of the classical Hitchin-Kobayashi correspondence, specially, we will focus on non-compact case; furthermore, We’ll discu...

One of the principal goals of spectral theory for operators is to find unitary invariants which are local relative to the spectrum. Multiplicity theory provides a complete set of such invariants for normal operators on (complex) Hilbert space. For general operators on finite-dimensional Hilbert space a nilpotent operator is attached to each point of the spectrum and these "local operators" toge...

AbstractHydroforming process is a deep stretching process only with the difference that a fluid is used instead of the mandrel. This paper investigates the hydroforming process of non-cylindrical and non-spherical geometries using finite element analysis software to calculate the influences of effective process parameters such as the coefficient of friction between the surfaces and the pressure...