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We prove the existence of quasi-projective coarse moduli spaces parametrising certain complete flags of subschemes of a fixed projective space $\mathbb{P}(V)$ up to projective automorphisms. The flags of subschemes being parametrised are obtained by intersecting non-degenerate subvarieties of $\mathbb{P}(V)$ of dimension $n$ by flags of linear subspaces of $\mathbb{P}(V)$ of length $n$, with each positive dimension component of the flags being required to be non-singular and non-degenerate, and with the dimension $0$ components being required to satisfy a Chow stability condition. These moduli spaces are constructed using non-reductive Geometric Invariant Theory for actions of groups whose unipotent radical is graded, making use of a non-reductive analogue of quotienting-in-stages developed by Hoskins and Jackson., Comment: Summary of changes in current version: corrected certain technical lemmas, improved exposition and introduction, addition of a section discussing similar possible constructions

We prove that any compactified universal Jacobian over any stack of stable maps, defined using torsion-free sheaves which are Gieseker semistable with respect to a relatively ample invertible sheaf over the universal curve, admits a projective good moduli space which can be constructed using GIT, and that the same is true for analogues parametrising semistable sheaves of higher rank. We also prove that for different choices of invertible sheaves, the corresponding good moduli spaces are related by a finite number of "Thaddeus flips". As a special case of our methods, we provide a new GIT construction of the universal Picard variety of Caporaso and Pandharipande., Comment: Summary of changes in current version: minor corrections and revisions

We prove various converse theorems for automorphic forms on \Gamma_0(N), each assuming fewer twisted functional equations than the last. We show that no twisting at all is needed for holomorphic modular forms in the case that N is 18, 20, or 24 - these integers are the smallest multiples of 4 or 9 not covered by earlier work of Conrey-Farmer. This development is a consequence of finding generating sets for \Gamma_0(N) such that each generator can be written as a product of special matrices. As for real-analytic Maass forms of even (resp. odd) weight we prove the analogous statement for N=1,...12,16,18 (resp. N=1,...,12,14,15,16,17,18,20,23,24)., Comment: 17 pages, 2 tables

The organic compounds of carbo- naceous chondrites are structurally diverse products of the prolonged abiotic chemistry that occurred before and during the early stages of the solar system [1]. They also represent the types of prebiotic compounds that may have participated in chemical evolutionary processes that gave rise to life [2]. Pyruvic acid is a key component of primary metabolism that has recently been found in carbonaceous chondrites [3]. Its prominence in biology has inspired us to explore its chemistry and possible role in the origin of metabolism. Our laboratory investigations have found that pyruvate (the ionized form of pyruvic acid) can serve as a single-source reactant to generate what we term a pyruvate reaction network (PRN). The core of the PRN is driven by pyruvate aldol polymerization and decay reactions. These decay reactions lead to the production of stable and unstable compounds which include mono, di, and tricarboxylic acids and a variety of keto acids. Finding evidence of this reaction network in meteorites would establish that the chemistry of pyruvate did occur in a prebiotic environment. Many of the known compounds found in pyruvate reaction mixtures were originally detected in meteorite samples by Cooper et al in 2011. However, multiple synthetic origins not tied to pyruvate chemistry might also explain their meteoritic presence. Thus, a search to find compounds unique to the PRN, such as reaction intermediates, would provide stronger evidence to demonstrate its prebiotic relevance. The identity of these intermediates can only be confirmed by acquiring chemical standards, however, as most are not available commercially, they need to be accessed through chemical synthesis.

These presentation slides introduce the Astrobiology Resource Metadata Standard (ARMS), a new metadata standard under development at NASA Ames Research Center, in conjunction with the Astrobiology Habitable Environments Database (AHED) project. The intent of this standard is to enable uniform, internet-based search and discovery of astrobiology 'resources', i.e. virtually any product of astrobiology research, including datasets, physical samples, software, publications, websites, images, video, presentations, etc. The current draft of ARMS defines 16 different metadata properties used to describe a given resource, including routine information such as name, resource type, description, personnel, funding, and related publications. But the true power in ARMS lies in four astrobiology-specific pieces of metadata: field site location enables geospatially-restricted search for resources using placenames or geospatial coordinates; research theme associates resources with one of six broad areas of astrobiological research (as identified in the 2015 NASA Astrobiology Strategy document); astrobiology disciplines captures the set of science disciplines most relevant to creation or use of resources; and finally, astrobiology keywords characterize resources in much in the same summarizing way that journal article keywords describe publications. An initial draft of the ARMS standard is being prepared for circulation to the astrobiology community for feedback and revision.

The organic compounds of carbonaceous chondrites are structurally diverse products of the prolonged abiotic chemistry that occurred before and during the early stages of the solar system. They also represent the types of prebiotic compounds that may have participated in chemical evolutionary processes that gave rise to life. Pyruvic acid is a key component of primary metabolism that has recently been found in carbonaceous chondrites. Its prominence in biology has inspired us to explore its chemistry and possible role in the origin of metabolism. Our laboratory investigations have found that pyruvate (the ionized form of pyruvic acid) can serve as a single-source reactant to generate what we term a pyruvate reaction network (PRN). The core of the PRN is driven by pyruvate aldol polymerization and decay reactions. These decay reactions lead to the production of stable and unstable compounds which include mono, di, and tricarboxylic acids and a variety of keto acids. Importantly, many of these reactions apparently lead back to pyruvate, establishing a feedback process. Finding evidence of this reaction network in meteorites would establish that the chemistry of pyruvate did occur in a prebiotic environment and indeed many of the known compounds found in pyruvate reaction mixtures were detected in the Murchison and Murray meteorites. However, multiple synthetic origins, not tied to pyruvate chemistry, might also explain their meteoritic presence. Thus finding compounds unique to the PRN, such as reaction intermediates, would provide stronger evidence in support of its prebiotic relevance. The identity of these intermediates can only be confirmed by acquiring chemical standards, however, as most are not available commercially, we engaged in extensive chemical synthesis. Obtaining these standards also provides the opportunity to study their subsequent chemistry and roles in the PRN.