The Berry curvature of the Bogoliubov quasiparticle Bloch states in the unconventional superconductor Sr2_2RuO4_4

We will extend the concept of electron band Berry curvatures to superconducting materials. We show that this can be defined for the Bogoliubov-de Gennes equation describing the superconducting state in a periodic crystal. In addition, the concept is exploited to understand the driving mechanism for the optical Kerr effect in time reversal symmetry breaking superconductors. Finally, we establish a sum rule analogue to the normal state Hall sum rule making quantitative contact between the imaginary part of the optical conductivity and the Berry curvature. The general theory will be applied and tested against the drosophila of the p-wave paired materials Sr$_2$RuO$_4$

Forget What?

One of a set of 3 cartoons, by James F. Martin, this one c. 1964. Depicts black male, with caption: Forget What?. In this print, there is a rendering of a black male wearing a Confederate grey hat and a Union blue coat. The figure is depicted as having a cane in his left hand. The person appears to be facing the center of the page.https://scholarsjunction.msstate.edu/fvw-artifacts/2412/thumbnail.jp

Letter from James Martin to Representative Burdick Regarding Garrison Dam Pool Level and Proposed Land Sales, February 16, 1955

This letter, dated February 16, 1955, from James F. Martin of the Buford Trenton East Valley Land Owners to United States (US) Representative Usher Burdick opens by stating that the land owners of the East Valley of the Buford-Trenton Irrigation Project are opposed to the proposed higher pool level for the Garrison Dam reservoir and dikes that would go with it. Martin then proposes that Congress buy the lands that the dikes would protect, as they could be had for the one third the cost of constructing dikes to protect them, and are not worth the expense of the dike system that is planned to protect them. There is a handwritten note on the back of the letter. See also: Letter from Representative Burdick to James Martin Regarding Garrison Dam Pool Level, February 18, 1955https://commons.und.edu/burdick-papers/1303/thumbnail.jp

Challenges in Reconciling Different Views of Neuroanatomy in a Reference Ontology of Anatomy

A fundamental requirement for integrating neuroscience data is a well-structured ontology that can incorporate, accommodate and reconcile different neuroanatomical views. Here we describe the challenges in creating such ontology, and, because of its principled design, illustrate the potential of the Foundational Model of Anatomy to be that ontology

Subgroups of direct products of limit groups

If $G_1,...,G_n$ are limit groups and $S\subset G_1\times...\times G_n$ is of type \FP_n(\mathbb Q) then $S$ contains a subgroup of finite index that is itself a direct product of at most $n$ limit groups. This settles a question of Sela.Comment: 20 pages, no figures. Final version. Accepted by the Annals of Mathematic

On the finite presentation of subdirect products and the nature of residually free groups

We establish {\em{virtual surjection to pairs}} (VSP) as a general criterion for the finite presentability of subdirect products of groups: if $\Gamma_1,...,\Gamma_n$ are finitely presented and $S<\Gamma_1\times...\times\Gamma_n$ projects to a subgroup of finite index in each $\Gamma_i\times\Gamma_j$, then $S$ is finitely presentable, indeed there is an algorithm that will construct a finite presentation for $S$. We use the VSP criterion to characterise the finitely presented residually free groups. We prove that the class of such groups is recursively enumerable. We describe an algorithm that, given a finite presentation of a residually free group, constructs a canonical embedding into a direct product of finitely many limit groups. We solve the (multiple) conjugacy problem and membership problem for finitely presentable subgroups of residually free groups. We also prove that there is an algorithm that, given a finite generating set for such a subgroup, will construct a finite presentation. New families of subdirect products of free groups are constructed, including the first examples of finitely presented subgroups that are neither ${\rm{FP}}_\infty$ nor of Stallings-Bieri typeComment: 44 pages. To appear in American Journal of Mathematics. This is a substantial rewrite of our previous Arxiv article 0809.3704, taking into account subsequent developments, advice of colleagues and referee's comment