Using a large sample of 90 Seyfert 2 galaxies (Sy2s) with spectropolarimetric observations, we tested the suggestion that the presence of hidden broad-line regions (HBLRs) in Sy2s is dependent upon the Eddington ratio. The stellar velocity dispersion and the extinction-corrected [O III] luminosity are used to derive the mass of central super-massive black holes and the Eddington ratio. We found...

Tropical Geometry by David E Speyer Doctor of Philosophy in Mathematics University of California, Berkeley Professor Bernd Sturmfels, Chair Let K be an algebraically closed field complete with respect to a nonarchimedean valuation v : K∗ → R. The reader should think ofK as the field of Puiseux series, ⋃∞ n=1 C((t )) and v as the map that assigns to a power series the exponent of its lowest degr...

Given a diagram of rings, one may consider the category of modules over them. We are interested in the homotopy theory of categories of this type: given a suitable diagram of model categories M(s) (as s runs through the diagram), we consider the category of diagrams where the object X(s) at s comes from M(s). We develop model structures on such categories of diagrams and Quillen adjunctions tha...

A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. ...

The observation that subjects who have a striking oral exostosis, called torus palatinus, also tended to have normal or high bone densities prompted us to examine an unselected population referred for bone density assessment for a possible correlation with torus palatinus. Subjects referred from community physicians had a visual examination of the open mouth to estimate the size of any torus pa...

We prove the logarithmic concavity of the Duistermaat-Heckman measure of an Hamiltonian (n− 2)-dimensional torus action for which there exists an effective commuting symplectic action of a 2-torus with symplectic orbits. Using this, we show that any symplectic (n− 2)-torus action with non-empty fixed point set which satisfies this additional 2-torus condition must be Hamiltonian.

We introduce the notion of a local torus action modeled on the standard representation (for simplicity, we call it a local torus action). It is a generalization of a locally standard torus action and also an underlying structure of a locally toric Lagrangian fibration. For a local torus action, we define two invariants called a characteristic pair and an Euler class of the orbit map, and prove ...