arXiv subjects

Mark McConnell

Publications and source records attributed to Mark McConnell.

24 records · Page 2Linked to original sources

arXiv2009

A Vigorous Explorer Program

Explorers have made breakthroughs in many fields of astrophysics. The science from both these missions contributed to three Nobel Prizes - Giacconi (2002), Mather, and Smoot (2006). Explorers have: marked the definitive beginning of precision cosmology, discovered that short gamma-ray bursts are caused by compact star mergers and have measured metalicity to redshifts z>6. NASA Explorers do cutting-edge science that cannot be done by facility-class instruments. The Explorer program provides a rapid response to changing science and technology, to enable cutting-edge science at moderate cost. Explorers also enable innovation, and engage & train scientists, managers and engineers, adding human capital to NASA and the nation. The astrophysics Explorer launch rate now being achieved is 1 per 3 years, and budget projections are in the $150M/year range for the next five years. A newly Vigorous Explorer Program should be created to: 1. Reach the long-stated goal of annual astrophysics launches; 2. Find additional launch options for Explorers and actively encourage cost savings in launchers and spacecraft, such as new commercial vehicles and innovative partnerships. 3. Mitigate risk via stronger technical development and sub-orbital programs, and through longer, more thorough, Phase A programs, potentially reducing the need for a 30% contingency; 4. Strive to protect the funding for missions that have reached Phase B, to prevent significant launch slips and cancellations, with a goal of 4 to 5 years from Phase B to launch; 5. Review the project management procedures and requirements to seek cost reductions, including the risk management strategy and the review and reporting process; 6. Review and possibly modify the cost caps for all Explorer classes to optimize scientific returns per dollar. [ABRIDGED]

astro-ph.IM↗

arXiv2009

Cohomology of Congruence Subgroups of SL_4(Z). III

In two previous papers [AGM1, AGM2] we computed cohomology groups H^5(Γ_0 (N); \C) for a range of levels N, where Γ_0 (N) is the congruence subgroup of SL_4 (\Z) consisting of all matrices with bottom row congruent to (0,0,0,*) mod N. In this note we update this earlier work by carrying it out for prime levels up to N = 211. This requires new methods in sparse matrix reduction, which are the main focus of the paper. Our computations involve matrices with up to 20 million non-zero entries. We also make two conjectures concerning the contributions to H^5(Γ_0 (N); \C) for N prime coming from Eisenstein series and Siegel modular forms.

math.NT↗

arXiv2007

Cohomology of Congruence Subgroups of SL(4,\Z) II

In a previous paper [3] we computed cohomology groups H^5 (Gamma_0 (N), \C), where Gamma_0 (N) is a certain congruence subgroup of SL (4, \Z), for a range of levels N. In this note we update this earlier work by extending the range of levels and describe cuspidal cohomology classes and additional boundary phenomena found since the publication of [3]. The cuspidal cohomology classes in this paper are the first cuspforms for GL(4) concretely constructed in terms of Betti cohomology.

math.NT↗

arXiv2006

The Advanced Compton Telescope Mission

The Advanced Compton Telescope (ACT), the next major step in gamma-ray astronomy, will probe the fires where chemical elements are formed by enabling high-resolution spectroscopy of nuclear emission from supernova explosions. During the past two years, our collaboration has been undertaking a NASA mission concept study for ACT. This study was designed to (1) transform the key scientific objectives into specific instrument requirements, (2) to identify the most promising technologies to meet those requirements, and (3) to design a viable mission concept for this instrument. We present the results of this study, including scientific goals and expected performance, mission design, and technology recommendations.

astro-ph↗

arXiv2000

Cohomology of congruence subgroups of SL(4,Z)

Let $N>1$ be an integer, and let $Γ= Γ_0 (N) \subset \SL_4 (\Z)$ be the subgroup of matrices with bottom row congruent to $(0,0,0,*)\mod N$. We compute $H^5 (Γ; \C) $ for a range of $N$, and compute the action of some Hecke operators on many of these groups. We relate the classes we find to classes coming from the boundary of the Borel-Serre compactification, to Eisenstein series, and to classical holomorphic modular forms of weights 2 and 4.

math.NT↗

arXiv1998

Hecke operators and Q-groups associated to self-adjoint homogeneous cones

Let G be a reductive algebraic group associated to a self-adjoint homogeneous cone defined over Q, and let G' be an appropriate neat arithmetic subgroup of G. We present two algorithms to compute the action of the Hecke operators on the integral cohomology of G'. This simultaneously generalizes the modular algorithm of Ash-Rudolph to a larger class of groups, and provides techniques to compute the Hecke-module structure of previously inaccessible cohomology groups.

math.NT↗