For Hierarchy in Animal Ethics

In my forthcoming book, How to Count Animals, More or Less (based on my 2016 Uehiro Lectures in Practical Ethics), I argue for a hierarchical approach to animal ethics according to which animals have moral standing but nonetheless have a lower moral status than people have. This essay is an overview of that book, drawing primarily from selections from its beginning and end, aiming both to give a feel for the overall project and to indicate the general shape of the hierarchical position that I defend there. In this essay, I contrast the hierarchical approach with its most important rival (which holds that people and animals have the very same moral status), sketch the main idea behind one central argument for hierarchy, and briefly review three potentially troubling implications of the hierarchical view. I close with a discussion of a promising possible solution to the most worrisome of the three objections

Academic underachievement: understanding and implications for educators

Includes bibliographical references

Monotonicity of Degrees of Generalized Alexander Polynomials of Groups and 3-Manifolds

We investigate the behavior of the higher-order degrees, db_n, of a finitely presented group G. These db_n are functions from H^1(G;Z) to Z whose values are the degrees certain higher-order Alexander polynomials. We show that if def(G) is at least 1 or G is the fundamental group of a compact, orientable 3-manifold then db_n is a monotonically increasing function of n for n at least 1. This is false for general groups. As a consequence, we show that if a 4 manifold of the form X times S^1 admits a symplectic structure then X ``looks algebraically like'' a 3-manifold that fibers over S^1, supporting a positive answer to a question of Taubes. This generalizes a theorem of S. Vidussi and is an improvement on the previous results of the author. We also find new conditions on a 3-manifold X which will guarantee that the Thurston norm of f*(psi), for psi in H^1(X;\Z) and f:Y -> X a surjective map on pi_1, will be at least as large the Thurston norm of psi. When X and Y are knot complements, this gives a partial answer to a question of J. Simon. More generally, we define Gamma-degrees, db_Gamma, corresponding to a surjective map G -> Gamma for which Gamma is poly-torsion-free-abelian. Under certain conditions, we show they satisfy a monotonicity condition if one varies the group. As a result, we show that these generalized degrees give obstructions to the deficiency of a group being positive and obstructions to a finitely presented group being the fundamental group of a compact, orientable 3-manifold.Comment: 19 page

Beauville surfaces and finite simple groups

A Beauville surface is a rigid complex surface of the form (C1 x C2)/G, where C1 and C2 are non-singular, projective, higher genus curves, and G is a finite group acting freely on the product. Bauer, Catanese, and Grunewald conjectured that every finite simple group G, with the exception of A5, gives rise to such a surface. We prove that this is so for almost all finite simple groups (i.e., with at most finitely many exceptions). The proof makes use of the structure theory of finite simple groups, probability theory, and character estimates.Comment: 20 page

New Beauville surfaces and finite simple groups

In this paper we construct new Beauville surfaces with group either \PSL(2,p^e), or belonging to some other families of finite simple groups of Lie type of low Lie rank, or an alternating group, or a symmetric group, proving a conjecture of Bauer, Catanese and Grunewald. The proofs rely on probabilistic group theoretical results of Liebeck and Shalev, on classical results of Macbeath and on recent results of Marion.Comment: v4: 18 pages. Final version, to appear in Manuscripta Mat

Beauville surfaces, moduli spaces and finite groups

In this paper we give the asymptotic growth of the number of connected components of the moduli space of surfaces of general type corresponding to certain families of Beauville surfaces with group either \PSL(2,p), or an alternating group, or a symmetric group or an abelian group. We moreover extend these results to regular surfaces isogenous to a higher product of curves.Comment: 27 pages. The article arXiv 0910.5402v2 was divided into two parts. This is the second half of the original paper, and it contains the subsections concerning the moduli spac

Commutator maps, measure preservation, and T-systems

Let G be a finite simple group. We show that the commutator map $a : G \times G \to G$ is almost equidistributed as the order of G goes to infinity. This somewhat surprising result has many applications. It shows that for a subset X of G we have $a^{-1}(X)/|G|^2 = |X|/|G| + o(1)$, namely $a$ is almost measure preserving. From this we deduce that almost all elements $g \in G$ can be expressed as commutators $g = [x,y]$ where x,y generate G. This enables us to solve some open problems regarding T-systems and the Product Replacement Algorithm (PRA) graph. We show that the number of T-systems in G with two generators tends to infinity as the order of G goes to infinity. This settles a conjecture of Guralnick and Pak. A similar result follows for the number of connected components of the PRA graph of G with two generators. Some of our results apply for more general finite groups, and more general word maps. Our methods are based on representation theory, combining classical character theory with recent results on character degrees and values in finite simple groups. In particular the so called Witten zeta function plays a key role in the proofs.Comment: 28 pages. This article was submitted to the Transactions of the American Mathematical Society on 21 February 2007 and accepted on 24 June 200