Derived Equivalences of K3 Surfaces and Twined Elliptic Genera

We use the unique canonically-twisted module over a certain distinguished super vertex operator algebra---the moonshine module for Conway's group---to attach a weak Jacobi form of weight zero and index one to any symplectic derived equivalence of a projective complex K3 surface that fixes a stability condition in the distinguished space identified by Bridgeland. According to work of Huybrechts, following Gaberdiel--Hohenegger--Volpato, any such derived equivalence determines a conjugacy class in Conway's group, the automorphism group of the Leech lattice. Conway's group acts naturally on the module we consider. In physics the data of a projective complex K3 surface together with a suitable stability condition determines a supersymmetric non-linear sigma model, and supersymmetry preserving automorphisms of such an object may be used to define twinings of the K3 elliptic genus. Our construction recovers the K3 sigma model twining genera precisely in all available examples. In particular, the identity symmetry recovers the usual K3 elliptic genus, and this signals a connection to Mathieu moonshine. A generalization of our construction recovers a number of the Jacobi forms arising in umbral moonshine. We demonstrate a concrete connection to supersymmetric non-linear K3 sigma models by establishing an isomorphism between the twisted module we consider and the vector space underlying a particular sigma model attached to a certain distinguished K3 surface.Comment: 62 pages including 7 pages of tables; updated references and minor editing in v.2; to appear in Research in the Mathematical Science

The Moonshine Module for Conway's Group

We exhibit an action of Conway's group---the automorphism group of the Leech lattice---on a distinguished super vertex operator algebra, and we prove that the associated graded trace functions are normalized principal moduli, all having vanishing constant terms in their Fourier expansion. Thus we construct the natural analogue of the Frenkel--Lepowsky--Meurman moonshine module for Conway's group. The super vertex operator algebra we consider admits a natural characterization, in direct analogy with that conjectured to hold for the moonshine module vertex operator algebra. It also admits a unique canonically-twisted module, and the action of the Conway group naturally extends. We prove a special case of generalized moonshine for the Conway group, by showing that the graded trace functions arising from its action on the canonically-twisted module are constant in the case of Leech lattice automorphisms with fixed points, and are principal moduli for genus zero groups otherwise.Comment: 54 pages including 11 pages of tables; minor revisions in v2, submitte

Upper Bound on the Dark Matter Total Annihilation Cross Section

We consider dark matter annihilation into Standard Model particles and show that the least detectable final states, namely neutrinos, define an upper bound on the total cross section. Calculating the cosmic diffuse neutrino signal, and comparing it to the measured terrestrial atmospheric neutrino background, we derive a strong and general bound. This can be evaded if the annihilation products are dominantly new and truly invisible particles. Our bound is much stronger than the unitarity bound at the most interesting masses, shows that dark matter halos cannot be significantly modified by annihilations, and can be improved by a factor of 10--100 with existing neutrino experiments.Comment: 4 pages, 3 figures; version accepted for publication in PR

The Table of Distribution and Allowances (TDA) system analyzer

TDA documents determine the personnel strengths for each Army installation. They reflect the number of people required to accomplish a certain mission by various characteristics. U.S. Army Training and Doctrine Command (TRADOC) analysts continuously scrutinize these documents to ensure that they comply with provided guidance. Part of this guidance has been used to develop a set of manual rules. Analysts apply these rules to the TDA to eliminate positions, downgrade positions, or reduce position strength. However, this process is very time consuming. ln addition, human involvement introduces inconsistencies and errors that are difficult to detect later. This paper explains how I represented these rules using the 'C' Language Production System (CLIPS) to develop an expert system that is applied consistently and comprehensively for all TRADOC installations. The TDA System Analyzer reduces the review process from about five days to just twenty minutes; giving the user more time to analyze the results and thereby make better decisions. Furthermore, the user is assured that the rules are applied uniformly to every TDA document. This paper also explains the integration of the TDA System Analyzer into TRADOC's On-Line TDA System. Providing the analyst an extra utility module that can be accessed from a familiar environment

Ensemble Concerts: Symphonic Band and Symphonic Winds, October 6, 2022

Center for the Performing ArtsOctober 6th, 2022Thursday Evening8:00 p.m

University Band, Symphonic Band, Symphonic Winds, November 16, 2021

Center for the Performing Arts November 16, 2021 Tuesday Evening 7:00 p.m

Wind Symphony, September 30, 2021

Center for the Performing Arts September 30, 2021 Thursday Evening 8:00 p.m

Ensemble Concerts: University Band and Symphonic Band, April 20, 2022

Center for the Performing Arts April 20, 2022 Wednesday Evening 8:00 p.m

Symphonic Winds, March 28, 2022

Center for the Performing Arts March 28, 2022 Monday Evening 8:00 p.m