Modularity of nearly ordinary 2-adic residually dihedral Galois representations

We prove modularity of some two dimensional, 2-adic Galois representations over totally real fields that are nearly ordinary and that are residually dihedral. We do this by employing the strategy of Skinner and Wiles, using Hida families, together with the 2-adic patching method of Khare and Wintenberger. As an application we deduce modularity of some elliptic curves over totally real fields that have good ordinary or multiplicative reduction at places above 2.Comment: 87 pages. Typos correcte

The Evolution of Language Groups among Cooperating Digital Predators

Many species of animals have evolved complex means for communicating with one another. Oftentimes, communication is essential for the execution of tasks that require cooperation between individuals, such as group hunting and mate selection. As a result, communication itself becomes essential for survival. While these facts are readily observed, the evolutionary processes underlying them are less understood, in large part because observational - much less controlled - studies of these processes are impossible. Both the timescales and population sizes required for such studies are simply too great. To address these problems, this thesis uses simulated predators to study the evolution of language in animals. These digital predators evolve to perform two cooperative tasks: hunting and mate selection. After the populations of predators have evolved to perform both tasks successfully, the population is decomposed into both language groups and cooperative groups. Spectral clustering identifies predators that speak similar languages, while merge clustering is used to find those groups of predators that are the most successful when working together. Analysis of the groups generated by these two different methods shows that the most successful pairings are not necessarily those in which the two individuals are speaking the same language. Rather, organisms can evolve to speak a different language than the one to which they respond. Moreover, even though one task -- mate selection -- evolves earlier in evolutionary history, the language diversity it produces counteracts any head-start provided for the evolution of the second task. Thus, not only is language important for the evolution of cooperative task success, but the appearance of language groups can also play a determinant role in the evolution of cooperation.Computer Science

Deformations of polarized automorphic Galois representations and adjoint Selmer groups

We prove the vanishing of the geometric Bloch-Kato Selmer group for the adjoint representation of a Galois representation associated to regular algebraic polarized cuspidal automorphic representations under an assumption on the residual image. Using this, we deduce that the localization and completion of a certain universal deformation ring for the residual representation at the characteristic zero point induced from the automorphic representation is formally smooth of the correct dimension. We do this by employing the Taylor-Wiles-Kisin patching method together with Kisin's technique of analyzing the generic fibre of universal deformation rings. Along the way we give a characterization of smooth closed points on the generic fibre of Kisin's potentially semistable local deformation rings in terms of their Weil-Deligne representations.Comment: Added reference to work of Breuil-Hellmann-Schraen. Minor change in assumption (b) of Theorems C and 3.1.3. Added Theorem 3.2.3 and subsection 3.3. Corrected typos and incorporated suggestions of the referee. To appear in Duke Math.

Flory-Huggins theory for the solubility of heterogeneously-modified polymers

Many water soluble polymers are chemically modified versions of insoluble base materials such as cellulose. A Flory-Huggins model is solved to determine the effects of heterogeneity in modification on the solubility of such polymers. It is found that heterogeneity leads to decreased solubility, with the effect increasing with increasing blockiness. In the limit of extreme blockiness, the nature of the phase coexistence crosses over to a polymer-polymer demixing transition. Some consequences are discussed for the synthesis of partially modified polymers, and the experimental characterisation of such systems.Comment: 4 pages, 2 figures, RevTeX 4.

A Balmer-line Broad Absorption Line Quasar

I report the discovery of blueshifted broad absorption line (BAL) troughs in at least six transitions of the Balmer series of hydrogen (Hbeta to H9) and in CaII, MgII and excited FeII in the quasar SDSS J125942.80+121312.6. This is only the fourth active galactic nucleus known to exhibit Balmer absorption, all four in conjunction with low-ionization BAL systems containing excited Fe II. The substantial population in the n=2 shell of H I in this quasar's absorber likely arises from Ly-alpha trapping. In an absorber sufficiently optically thick to show Balmer absorption, soft X-rays from the quasar penetrate to large \tau_Ly\alpha and ionize H I. Recombination then creates Ly-alpha photons that increase the n=2 population by a factor \tau_Ly\alpha since they require about \tau_Ly\alpha scatterings to diffuse out of the absorber. Observing Ly-alpha trapping in a quasar absorber requires a large but Compton-thin column of gas along our line of sight which includes substantial H I but not too much dust. Presumably the rarity of Balmer-line BAL troughs reflects the rarity of such conditions in quasar absorbers.Comment: AJ in press. 4 pages, 1 figure, 1 table, emulateapj forma