A second order algebraic knot concordance group

We define an algebraic group comprising symmetric chain complexes which captures the first two stages of the Cochran-Orr-Teichner solvable filtration of the knot concordance group in a single invariant. To achieve this we impose additional structure on each chain complex which puts extra control on the fundamental groups, and in particular on the way in which they can change in a concordance.Comment: 51 pages, 2 figures. This a considerably shortened version of arXiv:1109.0761, to appear in Algebraic and Geometric Topolog

An introduction to moduli stacks, with a view towards Higgs bundles on algebraic curves

This article is based in part on lecture notes prepared for the summer school "The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles" at the Institute for Mathematical Sciences at the National University of Singapore in July of 2014. The aim is to provide a brief introduction to algebraic stacks, and then to give several constructions of the moduli stack of Higgs bundles on algebraic curves. The first construction is via a "bootstrap" method from the algebraic stack of vector bundles on an algebraic curve. This construction is motivated in part by Nitsure's GIT construction of a projective moduli space of semi-stable Higgs bundles, and we describe the relationship between Nitsure's moduli space and the algebraic stacks constructed here. The third approach is via deformation theory, where we directly construct the stack of Higgs bundles using Artin's criterion.Comment: 145 pages, AMS LaTeX, to appear in the NUS IMS Lecture Note Series on The Geometry, Topology, and Physics of Moduli Spaces of Higgs Bundle

The Representation and Perception of Roman Imperial Power

Ancient history: to c 500 C