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

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.

Finiteness of unramified deformation rings

We prove that the universal unramified deformation ring $R^{\mathrm{unr}}$ of a continuous Galois representation $\overline{\rho}: G_{F^{+}} \rightarrow \mathrm{GL}_n(k)$ (for a totally real field $F^{+}$ and finite field $k$) is finite over $\mathcal{O} = W(k)$ in many cases. We also prove (under similar hypotheses) that the universal deformation ring $R^{\mathrm{univ}}$ is finite over the local deformation ring $R^{\mathrm{loc}}$.Comment: To appear in Algebra & Number Theor

Monodromy for some rank two Galois representations over CM fields

We investigate local-global compatibility for cuspidal automorphic representations $\pi$ for GL(2) over CM fields that are regular algebraic of weight $0$. We prove that for a Dirichlet density one set of primes $l$ and any $\iota : \overline{\mathbf{Q}}_l \cong \mathbf{C}$, the $l$-adic Galois representation attached to $\pi$ and $\iota$ has nontrivial monodromy at any $v \nmid l$ in $F$ at which $\pi$ is special.Comment: 15 page

Automorphy lifting for residually reducible ll-adic Galois representations, II

We prove new automorphy lifting theorems for residually reducible Galois representations of unitary type in which the residual representation is permitted to have an arbitrary number of irreducible constituents.Comment: Accepted versio

Phosphorylation of Spinophilin Modulates Its Interaction with Actin Filaments

Spinophilin is a protein phosphatase 1 (PP1)- and actin-binding protein that modulates excitatory synaptic transmission and dendritic spine morphology. We report that spinophilin is phosphorylated in vitro by protein kinase A (PKA). Phosphorylation of spinophilin was stimulated by treatment of neostriatal neurons with a dopamine D1 receptor agonist or with forskolin, consistent with spinophilin being a substrate for PKA in intact cells. Using tryptic phosphopeptide mapping, site-directed mutagenesis, and microsequencing analysis, we identified two major sites of phosphorylation, Ser-94 and Ser-177, that are located within the actin-binding domain of spinophilin. Phosphorylation of spinophilin by PKA modulated the association between spinophilin and the actin cytoskeleton. Following subcellular fractionation, unphosphorylated spinophilin was enriched in the postsynaptic density, whereas a pool of phosphorylated spinophilin was found in the cytosol. F-actin co-sedimentation and overlay analysis revealed that phosphorylation of spinophilin reduced the stoichiometry of the spinophilin-actin interaction. In contrast, the ability of spinophilin to bind to PP1 remained unchanged. Taken together, our studies suggest that phosphorylation of spinophilin by PKA modulates the anchoring of the spinophilin-PP1 complex within dendritic spines, thereby likely contributing to the efficacy and plasticity of synaptic transmission

Mechanically-stacked tandem solar cells with GaAsP on GaP and silicon

Preliminary results are encouraging for the achievement of high conversion efficiencies using a GaAsP top solar cell mechanically stacked on a conventional silicon solar cell. A realistic maximum of 29.4 percent is suggested when both the top and bottom solar cells are state of the art. Practical system efficiencies greater than 25 percent are attainable in the near future with the use of a state of the art bottom solar cell

Sampling rare switching events in biochemical networks

Bistable biochemical switches are ubiquitous in gene regulatory networks and signal transduction pathways. Their switching dynamics, however, are difficult to study directly in experiments or conventional computer simulations, because switching events are rapid, yet infrequent. We present a simulation technique that makes it possible to predict the rate and mechanism of flipping of biochemical switches. The method uses a series of interfaces in phase space between the two stable steady states of the switch to generate transition trajectories in a ratchet-like manner. We demonstrate its use by calculating the spontaneous flipping rate of a symmetric model of a genetic switch consisting of two mutually repressing genes. The rate constant can be obtained orders of magnitude more efficiently than using brute-force simulations. For this model switch, we show that the switching mechanism, and consequently the switching rate, depends crucially on whether the binding of one regulatory protein to the DNA excludes the binding of the other one. Our technique could also be used to study rare events and non-equilibrium processes in soft condensed matter systems.Comment: 9 pages, 6 figures, last page contains supplementary informatio