Eigenvectors of tensors - A primer

We give an introduction to the theory and to some applications of eigenvectors of tensors (in other words, invariant one-dimensional subspaces of homogeneous polynomial maps), including a review of some concepts that are useful for their discussion. The intent is to give practitioners an overview of fundamental notions, results and techniques

Building the red sequence through gas-rich major mergers

Understanding the details of how the red sequence is built is a key question in galaxy evolution. What are the relative roles of gas-rich vs. dry mergers, major vs. minor mergers or galaxy mergers vs. gas accretion? In Wild et al. 2009 we compare hydrodynamic simulations with observations to show how gas-rich major mergers result in galaxies with strong post-starburst spectral features, a population of galaxies easily identified in the real Universe using optical spectra. Using spectra from the VVDS deep survey with z~0.7, and a principal component analysis technique to provide indices with high enough SNR, we find that 40% of the mass flux onto the red-sequence could enter through a strong post-starburst phase, and thus through gas-rich major mergers. The deeper samples provided by next generation galaxy redshift surveys will allow us to observe the primary physical processes responsible for the shut-down in starformation and build-up of the red sequence.Comment: 4 pages, 7 figures, proceedings of IAU symposium 262 "Stellar populations, planning for the next decade

Rational Conformal Field Theories With G_2 Holonomy

We study conformal field theories for strings propagating on compact, seven-dimensional manifolds with G_2 holonomy. In particular, we describe the construction of rational examples of such models. We argue that analogues of Gepner models are to be constructed based not on N=1 minimal models, but on Z_2 orbifolds of N=2 models. In Z_2 orbifolds of Gepner models times a circle, it turns out that unless all levels are even, there are no new Ramond ground states from twisted sectors. In examples such as the quintic Calabi-Yau, this reflects the fact that the classical geometric orbifold singularity can not be resolved without violating G_2 holonomy. We also comment on supersymmetric boundary states in such theories, which correspond to D-branes wrapping supersymmetric cycles in the geometry.Comment: 20 pages, harvmac(b); v2: ref. adde

On the unipotence of autoequivalences of toric complete intersection Calabi-Yau categories

We identify a class of autoequivalences of triangulated categories of singularities associated with Calabi-Yau complete intersections in toric varieties. Elements of this class satisfy relations that are directly linked to the toric data.Comment: 17 page

Matrix Factorizations and Kauffman Homology

The topological string interpretation of homological knot invariants has led to several insights into the structure of the theory in the case of sl(N). We study possible extensions of the matrix factorization approach to knot homology for other Lie groups and representations. In particular, we introduce a new triply graded theory categorifying the Kauffman polynomial, test it, and predict the Kauffman homology for several simple knots.Comment: 45 pages, harvma

Coordinate-independent singular perturbation reduction for systems with three time scales

On the basis of recent work by Cardin and Teixeira on ordinary differential equations with more than two time scales, we devise a coordinate-independent reduction for systems with three time scales; thus no a priori separation of variables into fast, slow etc. is required. Moreover we consider arbitrary parameter dependent systems and extend earlier work on Tikhonov-Fenichel parameter values -- i.e. parameter values from which singularly perturbed systems emanate upon small perturbations -- to the three time-scale setting. We apply our results to two standard systems from biochemistry

Long Range Structure of the Nucleon

The long range structure of the nucleon is discussed starting from the old model of a quark bag with a pion cloud (``cloudy bag'') carrying on to the more recent ideas of the parton model of the nucleon. On the basis of the most recent measurements of the form factors at MAMI, JLab and MIT quantitative results for nucleon charge densities are presented within both non-relativistic and relativistic frameworks.Comment: 14 pages, 14 figure