On a question of Bumagin and Wise

Motivated by a question of Bumagin and Wise, we construct a continuum of finitely generated, residually finite groups whose outer automorphism groups are pairwise non-isomorphic finitely generated, non-recursively-presentable groups. These are the first examples of such residually finite groups.Comment: 8 page

On the outer automorphism groups of finitely generated, residually finite groups

Bumagin-Wise posed the question of whether every countable group can be realised as the outer automorphism group of a finitely generated, residually finite group. We give a partial answer to this problem for recursively presentable groups.Comment: 13 pages. Final versio

Every group is the outer automorphism group of an HNN-extension of a fixed triangle group

Fix an equilateral triangle group $T_i=\langle a, b; a^i, b^i, (ab)^i\rangle$ with $i\geq6$ arbitrary. Our main result is: for every presentation $\mathcal{P}$ of every countable group $Q$ there exists an HNN-extension $T_{\mathcal{P}}$ of $T_i$ such that $\operatorname{Out}(T_{\mathcal{P}})\cong Q$. We construct the HNN-extensions explicitly, and examples are given. The class of groups constructed have nice categorical and residual properties. In order to prove our main result we give a method for recognising malnormal subgroups of small cancellation groups, and we introduce the concept of "malcharacteristic" subgroups.Comment: 39 pages. Final version, to appear in Advances in Mathematic

The Outer Automorphism Groups of Two-Generator One-Relator Groups with Torsion

The main result of this paper is a complete classification of the outer automorphism groups of two-generator, one-relator groups with torsion. To this classification we apply recent algorithmic results of Dahmani--Guirardel, which yields an algorithm to compute the isomorphism class of the outer automorphism group of a given two-generator, one-relator group with torsion.Comment: 15 pages, final version. To appear in Proc. Amer. Math. So

Magnetic properties of the Anderson model: a local moment approach

We develop a local moment approach to static properties of the symmetric Anderson model in the presence of a magnetic field, focussing in particular on the strong coupling Kondo regime. The approach is innately simple and physically transparent; but is found to give good agreement, for essentially all field strengths, with exact results for the Wilson ratio, impurity magnetization, spin susceptibility and related properties.Comment: 7 pages, 3 postscript figues. Latex 2e using the epl.cls Europhysics Letters macro packag

Whoa, Nellie! Empirical Tests of College Football's Conventional Wisdom

College football fans, coaches, and observers have adopted a set of beliefs about how college football poll voters behave. I document three pieces of conventional wisdom in college football regarding the timing of wins and losses, the value of playing strong opponents, and the value of winning by wide margins. Using a unique data set with 25 years of AP poll results, I test college football's conventional wisdom. In particular, I test (1) whether it is better to lose early or late in the season, (2) whether teams benefit from playing stronger opponents, and (3) whether teams are rewarded for winning by large margins. Contrary to conventional wisdom, I find that (1) it is better to lose later in the season than earlier, (2) AP voters do not pay attention to the strength of a defeated opponent, and (3) the benefit of winning by a large margin is negligible. I conclude by noting how these results inform debates about a potential playoff in college football.

Spectral scaling and quantum critical behaviour in the pseudogap Anderson model

The pseudogap Anderson impurity model provides a classic example of an essentially local quantum phase transition. Here we study its single-particle dynamics in the vicinity of the symmetric quantum critical point (QCP) separating generalized Fermi liquid and local moment phases, via the local moment approach. Both phases are shown to be characterized by a low-energy scale that vanishes at the QCP; and the universal scaling spectra, on all energy scales, are obtained analytically. The spectrum precisely at the QCP is also obtained; its form showing clearly the non-Fermi liquid, interacting nature of the fixed point.Comment: 7 pages, 2 figure

A spin-dependent local moment approach to the Anderson impurity model

We present an extension of the local moment approach to the Anderson impurity model with spin-dependent hybridization. By employing the two-self-energy description, as originally proposed by Logan and co-workers, we applied the symmetry restoration condition for the case with spin-dependent hybridization. Self-consistent ground states were determined through variational minimization of the ground state energy. The results obtained with our spin-dependent local moment approach applied to a quantum dot system coupled to ferromagnetic leads are in good agreement with those obtained from previous work using numerical renormalization group calculations