Curve-counting invariants for crepant resolutions

We construct curve counting invariants for a Calabi-Yau threefold $Y$ equipped with a dominant birational morphism $\pi:Y \to X$. Our invariants generalize the stable pair invariants of Pandharipande and Thomas which occur for the case when $\pi:Y\to Y$ is the identity. Our main result is a PT/DT-type formula relating the partition function of our invariants to the Donaldson-Thomas partition function in the case when $Y$ is a crepant resolution of $X$, the coarse space of a Calabi-Yau orbifold $\mathcal{X}$ satisfying the hard Lefschetz condition. In this case, our partition function is equal to the Pandharipande-Thomas partition function of the orbifold $\mathcal{X}$. Our methods include defining a new notion of stability for sheaves which depends on the morphism $\pi$. Our notion generalizes slope stability which is recovered in the case where $\pi$ is the identity on $Y$. Our proof is a generalization of Bridgeland's proof of the PT/DT correspondence via the Hall algebra and Joyce's integration map.Comment: In this version, Jim Bryan has been added as an author and the required boundedness result for our stability condition has been added. arXiv admin note: text overlap with arXiv:1002.4374 by other author

How the Marsden Fund has failed to achieve its full potential in the ESA panel: evidence of limitations in scope, biased outcomes, and futile applications

We have analysed the scope of proposals funded by the ‘Earth Sciences and Astronomy’ (ESA) panel of the Marsden Fund for the period 2004 to 2013. The scope of proposals funded is very limited and does not reflect the full remit of the panel: the successful projects fail to encompass the quality and quantity of research being undertaken within the Earth sciences community in New Zealand, and a number of sub-disciplines that seek to address fundamental and important problems within the Earth sciences are largely excluded. Moreover, nearly 50% of the funded proposals for the past decade have been made to just two institutions. To address these limitations, we suggest that: (1) a review is undertaken to examine and widen the scope of the panel to encompass sub-disciplines that demonstrably are never or rarely funded; (2) the composition of panel members be examined and modified to reflect a much wider scope of sub-disciplines within the Earth sciences; and (3) a review of the wide discrepancies in funding distributions on an institutional basis be undertaken. We want to ensure that a more representative range of sub-disciplines, in keeping with modern and realistic definitions of the Earth sciences, is funded through this panel, and so we also recommend the formation of a new panel for ‘Environmental and Earth-system Sciences’ that could encompass the research involving modern-day processes so that applications in these sub-disciplines are not pointless. In addition, it is clear that a very substantial increase in funding to the Marsden Fund must be sought

Can conventional theory explain the unconventional recovery?

An argument that the sluggishness of the current economic recovery reflects a permanent, structural change in the economy that may not be easily addressed using the standard monetary/fiscal incentives called for in the conventional view of business cycles, and that structural adjustment is a critical component of all economic fluctuations.Business cycles ; Economic conditions - United States

Hang With Your Buddies to Resist Intersection Attacks

Some anonymity schemes might in principle protect users from pervasive network surveillance - but only if all messages are independent and unlinkable. Users in practice often need pseudonymity - sending messages intentionally linkable to each other but not to the sender - but pseudonymity in dynamic networks exposes users to intersection attacks. We present Buddies, the first systematic design for intersection attack resistance in practical anonymity systems. Buddies groups users dynamically into buddy sets, controlling message transmission to make buddies within a set behaviorally indistinguishable under traffic analysis. To manage the inevitable tradeoffs between anonymity guarantees and communication responsiveness, Buddies enables users to select independent attack mitigation policies for each pseudonym. Using trace-based simulations and a working prototype, we find that Buddies can guarantee non-trivial anonymity set sizes in realistic chat/microblogging scenarios, for both short-lived and long-lived pseudonyms.Comment: 15 pages, 8 figure