The Quantum McKay Correspondence for polyhedral singularities

Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity C^3/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over the positive roots of R. In terms of counts of BPS states (Gopakumar-Vafa invariants), our result can be stated as a correspondence: each positive root of R corresponds to one half of a genus zero BPS state. As an application, we use the crepant resolution conjecture to provide a full prediction for the orbifold Gromov-Witten invariants of [C^3/G].Comment: Introduction rewritten. Issue regarding non-uniqueness of conifold resolution clarified. Version to appear in Inventione

Collective Interview on the History of Town Meetings

As illustrated in the introduction, the special issue ends with a ‘collective interview’ to some distinguished scholars that have given an important contribution to the study of New England Town Meetings. The collective interview has been realized by submitting three questions to our interviewees, who responded individually in written. The text of the answers has not been edited, if not minimally. However, the editors have broken up longer individual answers in shorter parts. These have been subsequently rearranged in an effort to provide, as much as possible, a fluid structure and a degree of interaction among the different perspectives provided by our interviewees on similar issues. The final version of this interview has been edited and approved by all interviewees

Evidence for the intense exchange of MazG in marine cyanophages by horizontal gene transfer

Background: S-PM2 is a phage capable of infecting strains of unicellular cyanobacteria belonging to the genus Synechococcus. S-PM2, like other myoviruses infecting marine cyanobacteria, encodes a number of bacterial-like genes. Amongst these genes is one encoding a MazG homologue that is hypothesized to be involved in the adaption of the infected host for production of progeny phage. Methodology/Principal Findings: This study focuses on establishing the occurrence of mazG homologues in other cyanophages isolated from different oceanic locations. Degenerate PCR primers were designed using the mazG gene of S-PM2. The mazG gene was found to be widely distributed and highly conserved among Synechococcus myoviruses and podoviruses from diverse oceanic provinces. Conclusions/Significance: This study provides evidence of a globally connected cyanophage gene pool, the cyanophage mazG gene having a small effective population size indicative of rapid lateral gene transfer despite being present in a substantial fraction of cyanophage. The Prochlorococcus and Synechococcus phage mazG genes do not cluster with the host mazG gene, suggesting that their primary hosts are not the source of the mazG gene

Grassmann phase space theory for fermions

A phase space theory for fermions has been developed using Grassmann phase space variables which can be used in numerical calculations for cold Fermi gases and for large fermion numbers. Numerical calculations are feasible because Grassmann stochastic variables at later times are related linearly to such variables at earlier times via c-number stochastic quantities. A Grassmann field version has been developed making large fermion number applications possible. Applications are shown for few mode and field theory cases