Derived categories of cubic fourfolds

We discuss the structure of the derived category of coherent sheaves on cubic fourfolds of three types: Pfaffian cubics, cubics containing a plane and singular cubics, and discuss its relation to the rationality of these cubics.Comment: 18 page

Geometric invariant theory of syzygies, with applications to moduli spaces

We define syzygy points of projective schemes, and introduce a program of studying their GIT stability. Then we describe two cases where we have managed to make some progress in this program, that of polarized K3 surfaces of odd genus, and of genus six canonical curves. Applications of our results include effectivity statements for divisor classes on the moduli space of odd genus K3 surfaces, and a new construction in the Hassett-Keel program for the moduli space of genus six curves.Comment: v1: 23 pages, submitted to the Proceedings of the Abel Symposium 2017, v2: final version, corrects a sign error and resulting divisor class calculations on the moduli space of K3 surfaces in Section 5, other minor changes, In: Christophersen J., Ranestad K. (eds) Geometry of Moduli. Abelsymposium 2017. Abel Symposia, vol 14. Springer, Cha

Fibrations on four-folds with trivial canonical bundles

Four-folds with trivial canonical bundles are divided into six classes according to their holonomy group. We consider examples that are fibred by abelian surfaces over the projective plane. We construct such fibrations in five of the six classes, and prove that there is no such fibration in the sixth class. We classify all such fibrations whose generic fibre is the Jacobian of a genus two curve.Comment: 28 page

Characterization of a fluidized-bed combustion ash to determine potential for environmental impact. Final report

A 440-megawatt, circulating fluidized-bed combustion (CFBC), lignite-fired power plant is planned for construction in Choctaw County north of Ackerman, Mississippi. This power plant will utilize Mississippi lignite from the first lignite mine in that state. Malcolm Pirnie, Inc., is working with the power plant developer in the current planning and permitting efforts for this proposed construction project. In order to accommodate Mississippi state regulatory agencies and meet appropriate permit requirements, Malcolm Pirnie needed to provide an indication of the characteristics of the by-products anticipated to be produced at the proposed plant. Since the Mississippi lignite is from a newly tapped mine and the CFBC technology is relatively new, Malcolm Pirnie contacted with the Energy and Environmental Research Center (EERC) to develop and perform a test plan for the production and characterization of ash similar to ash that will be eventually produced at the proposed power plant. The work performed at the EERC included two primary phases: production of by-products in a bench-scale CFBC unit using lignite provided by Malcolm Pirnie with test conditions delineated by Malcolm Pirnie to represent expected operating conditions for the full-scale plant; and an extensive characterization of the by-products produced, focusing on Mississippi regulatory requirements for leachability, with the understanding that return of the by-product to the mine site was an anticipated by-product management plan. The overall focus of this project was the environmental assessment of the by-product expected to be produced at the proposed power plant. Emphasis was placed on the leachability of potentially problematic trace elements in the by-products. The leaching research documented in this report was performed to determine trends of leachability of trace elements under leaching conditions appropriate for evaluating land disposal in monofills, such as returning the by-products to the mine site

An extremal effective survey about extremal effective cycles in moduli spaces of curves

We survey recent developments and open problems about extremal effective divisors and higher codimension cycles in moduli spaces of curves.Comment: Submitted to the Proceedings of the Abel Symposium 2017. Comments are welcom

The Anti-Sigma Factor MucA of Pseudomonas aeruginosa: Dramatic Differences of a mucA22 vs. a ΔmucA Mutant in Anaerobic Acidified Nitrite Sensitivity of Planktonic and Biofilm Bacteria in vitro and During Chronic Murine Lung Infection

Mucoid mucA22 Pseudomonas aeruginosa (PA) is an opportunistic lung pathogen of cystic fibrosis (CF) and chronic obstructive pulmonary disease (COPD) patients that is highly sensitive to acidified nitrite (A-NO2-). In this study, we first screened PA mutant strains for sensitivity or resistance to 20 mM A-NO2- under anaerobic conditions that represent the chronic stages of the aforementioned diseases. Mutants found to be sensitive to A-NO2- included PA0964 (pmpR, PQS biosynthesis), PA4455 (probable ABC transporter permease), katA (major catalase, KatA) and rhlR (quorum sensing regulator). In contrast, mutants lacking PA0450 (a putative phosphate transporter) and PA1505 (moaA2) were A-NO2- resistant. However, we were puzzled when we discovered that mucA22 mutant bacteria, a frequently isolated mucA allele in CF and to a lesser extent COPD, were more sensitive to A-NO2- than a truncated ΔmucA deletion (Δ157–194) mutant in planktonic and biofilm culture, as well as during a chronic murine lung infection. Subsequent transcriptional profiling of anaerobic, A-NO2--treated bacteria revealed restoration of near wild-type transcript levels of protective NO2- and nitric oxide (NO) reductase (nirS and norCB, respectively) in the ΔmucA mutant in contrast to extremely low levels in the A-NO2--sensitive mucA22 mutant. Proteins that were S-nitrosylated by NO derived from A-NO2- reduction in the sensitive mucA22 strain were those involved in anaerobic respiration (NirQ, NirS), pyruvate fermentation (UspK), global gene regulation (Vfr), the TCA cycle (succinate dehydrogenase, SdhB) and several double mutants were even more sensitive to A-NO2-. Bioinformatic-based data point to future studies designed to elucidate potential cellular binding partners for MucA and MucA22. Given that A-NO2- is a potentially viable treatment strategy to combat PA and other infections, this study offers novel developments as to how clinicians might better treat problematic PA infections in COPD and CF airway diseases

recA and catalase in H2O2-mediated toxicity in Neisseria gonorrhoeae.

Neisseria gonorrhoeae cells defective in the biosynthesis of the recA gene product are no more sensitive to hydrogen peroxide than wild-type cells. Although gonococci possess nearly 100-fold-greater catalase levels than Escherichia coli, they are more susceptible to hydrogen peroxide than this organism. The natural niche of gonococci undoubtedly results in exposure to oxidant stress; however, they do not demonstrate particularly efficient antioxidant defense systems

Complete moduli of cubic threefolds and their intermediate Jacobians

The intermediate Jacobian map, which associates to a smooth cubic threefold its intermediate Jacobian, does not extend to the GIT compactification of the space of cubic threefolds, not even as a map to the Satake compactification of the moduli space of principally polarized abelian fivefolds. A much better "wonderful" compactification of the space of cubic threefolds was constructed by the first and fourth authors --- it has a modular interpretation, and divisorial normal crossing boundary. We prove that the intermediate Jacobian map extends to a morphism from the wonderful compactification to the second Voronoi toroidal compactification of the moduli of principally polarized abelian fivefolds --- the first and fourth author previously showed that it extends to the Satake compactification. Since the second Voronoi compactification has a modular interpretation, our extended intermediate Jacobian map encodes all of the geometric information about the degenerations of intermediate Jacobians, and allows for the study of the geometry of cubic threefolds via degeneration techniques. As one application we give a complete classification of all degenerations of intermediate Jacobians of cubic threefolds of torus rank 1 and 2.Comment: 56 pages; v2: multiple updates and clarification in response to detailed referee's comment

Stability conditions and positivity of invariants of fibrations

We study three methods that prove the positivity of a natural numerical invariant associated to $1-$parameter families of polarized varieties. All these methods involve different stability conditions. In dimension 2 we prove that there is a natural connection between them, related to a yet another stability condition, the linear stability. Finally we make some speculations and prove new results in higher dimension.Comment: Final version, to appear in the Springer volume dedicated to Klaus Hulek on the occasion of his 60-th birthda

Reassessing the Social Returns to Equipment Investment

The recent literature on the sources of economic growth has challenged the traditional growth accounting of the Solow model, which assigned a relatively limited role to capital deepening. As part of this literature, De Long and Summers have argued in two papers that the link between equipment investment and economic growth across countries is stronger than can be generated by the Solow model. Accordingly, they conclude that such investment yields important external benefits. However, their analysis suffers from two shortcomings. First, De Long and Summers have not conducted any formal statistical tests of the Solow model. Second, even their informal rejection of the model fails to survive reasonable tests of robustness. We formally test the predictions of the Solow model using De Long and Summers' data. Our results cast doubt on the existence of externalities to equipment investment. In particular, we find that the empirical link between investment and growth in the OECD countries is fully consistent with the Solow model. Moreover, for De Long and Summers' full sample, the evidence of excess returns to equipment investment is tenuous.