Derived traces of Soergel categories

We study two kinds of categorical traces of (monoidal) dg categories, with particular interest in categories of Soergel bimodules. First, we explicitly compute the usual Hochschild homology, or derived vertical trace, of the category of Soergel bimodules in arbitrary types. Secondly, we introduce the notion of derived horizontal trace of a monoidal dg category and compute the derived horizontal trace of Soergel bimodules in type A. As an application we obtain a derived annular Khovanov-Rozansky link invariant with an action of full twist insertion, and thus a categorification of the HOMFLY-PT skein module of the solid torus

A polynomial action on colored sl2sl_2 link homology

We construct an action of a polynomial ring on the colored sl(2) link homology of Cooper-Krushkal, over which this homology is finitely generated. We define a new, related link homology which is finite dimensional, extends to tangles, and categorifies a scalar-multiple of the sl(2) Reshetikhin-Turaev invariant. We expect this homology to be functorial under 4-dimensional cobordisms. The polynomial action is related to a conjecture of Gorsky-Oblomkov-Rasmussen-Shende on the stable Khovanov homology of torus knots, and as an application we obtain a weak version of this conjecture. A key new ingredient is the construction of a bounded chain complex which categorifies a scalar multiple of the Jones-Wenzl projector, in which the denominators have been cleared

On the functoriality of sl₂ tangle homology

We construct an explicit equivalence between the (bi)category of gl2 webs and foams and the Bar-Natan (bi)category of Temperley–Lieb diagrams and cobordisms. With this equivalence we can fix functoriality of every link homology theory that factors through the Bar-Natan category. To achieve this, we define web versions of arc algebras and their quasihereditary covers, which provide strictly functorial tangle homologies. Furthermore, we construct explicit isomorphisms between these algebras and the original ones based on Temperley–Lieb cup diagrams. The immediate application is a strictly functorial version of the Beliakova–Putyra–Wehrli quantization of the annular link homology

Can Silicon-Smelting Contribute to the Low O/Si Ratio on the Surface of Mercury?

The MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft collected data that provided important insights into the structure, chemical makeup, and compositional diversity of Mercury. Among the many discoveries about Mercury made by MESSENGER, several surprising compositional characteristics of the surface were observed. These discoveries include elevated sulfur abundances (up to 4 wt.%), elevated abundances of graphitic carbon (0-4.1 wt.% across the surface with an additional 1-3 wt.% graphite above the global average in low reflectance materials), low iron abundances (less than 2 wt.%), and low oxygen abundances (O/Si weight ratio of 1.20+/-0.1). These exotic characteristics likely have important implications for the thermochemical evolution of Mercury and point to a planet that formed under highly reducing conditions. In the present study, we focus specifically on the low O/Si ratio of Mercury, which is anomalous compared to all other planetary materials. A recent study that considered the geochemical implications of the low O/Si ratio reported that 12-20% of the surface materials on Mercury are composed of Si-rich, Si-Fe alloys. They further postulated that the origin of the metal is best explained by a combination of space weathering and graphite-induced smelting that was facilitated by interaction of graphite with boninitic and komatiitic parental liquids. The goal of the present study is to assess the plausibility of smelting on Mercury through experiments run at the conditions that McCubbin et al. indicated would be favorable for Si-smelting

An Expanded Stratigraphic Record of the Devonian-Carboniferous Boundary Hangenberg Biogeochemical Event from Southeast Iowa (U.S.A.)

The Devonian-Carboniferous boundary in the type area of the Mississippian subsystem (tri-state area of Iowa, Illinois, and Missouri) has been historically difficult to identify. Many of the localities contain similar lithologies and stratigraphic successions, but chronostratigraphic correlation of seemingly identical lithologies can vary greatly in this interval and frequently this has led to miscorrelation. In particular, the similar lithofacies that comprise the McCraney Formation and Louisiana Formation have been a source of stratigraphic confusion for over 100 years. To investigate the Devonian-Carboniferous boundary interval in the Mississippian type area we selected two localities in southeastern Iowa, the H-28 core from Lee County outside of Keokuk, Iowa, and the Starr’s Cave outcrop located near Burlington, Iowa. In total, 62 conodont samples and 299 carbonate carbon isotope samples were processed for this study and recorded the Hangenberg positive carbon isotope excursion and 25 conodont species, including a diverse assemblage of siphonodellids. The Hangenberg excursion is recorded in over 20 m of strata in southeast Iowa, making this one of the thickest stratigraphic records of this important biogeochemical event yet recovered, and helps to define more clearly the position of the base of the Carboniferous System in the region. These results show that the “McCraney” Fm. at the Starr’s Cave outcrop and the coeval carbonate unit in the H-28 core are both the Louisiana Formation, and calls into question the use of the name McCraney throughout the State of Iowa

Genetic variation in the myeloperoxidase gene and cognitive impairment in Multiple Sclerosis

There is evidence that multiple sclerosis (MS) may associated with cognitive impairment in 25 to 40% of cases. The gene encoding myeloperoxidase (MPO) is involved in molecular pathways leading to β-amyloid deposition. We investigated a functional biallelic (G/A) polymorphism in the promoter region (-463) of the MPO gene in 465 patients affected by MS, divided into 204 cognitively normal and 261 impaired. We did not find significant differences in allele or genotype distributions between impaired and preserved MS patients. Our findings suggest that MPO polymorphism is not a risk factor for cognitive impairment in MS

Evolved Gas Analyses of Mudstones from the Vera Rubin Ridge

The Sample Analysis at Mars (SAM) instrument suite on the Mars Science Laboratory (MSL) rover has been essential in understanding volatile-bearing phases in Gale Crater materials. SAMs evolved gas analysis mass spectrometry (EGA-MS) has detected H2O, CO2, O2, H2, SO2, H2S, HCl, NO, and other trace gases, including organic fragments, in many samples. The identity and evolution temperature of evolved gases can support CheMin instrument mineral detection and place constraints on trace volatile-bearing phases or phases difficult to characterize with X-ray diffraction (e.g., amorphous phases). For the past ~500 sols, MSL has been exploring the Vera Rubin Ridge (VRR), which exhibits a striking hematite signature in orbital remote sensing data, in order to understand the depositional and diagenetic history recorded in the rocks and how it relates to the underlying Murray Formation. Four rock samples were drilled, one from the Blunts Point Member (Duluth, DU), one from the Pettegrrove Point Member (Stoer, ST), and two from the Jura Member. The Jura Member displays differences in color, summarized as grey and red, and a key goal was to constrain the cause of this color difference and the associated implications for depositional or post-depositional conditions. To investigate, a grey (Highfield, HF) and a red (Rock Hall, RH) Jura sample were drilled. Here we will give an overview of results from SAM EGA-MS analyses of VRR materials, with some comparisons to analyses of samples of the underlying Murray