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The monotone wrapped Fukaya category and the open-closed string map
(SpringerSelecta Mathematica, 2016-08-09)
We build the wrapped Fukaya category $\textit{W}$($\textit{E}$)for any monotone symplectic manifold $\textit{E}$, convex at infinity. We define the open-closed and closed-open string maps, OC : HH$_{*}$($\textit{W}$($\textit{E}$)) ...
Automorphy of some residually S$_5$ Galois representations
(SpringerMathematische Zeitschrift, 2016)
Let $\textit{F}$ be a totally real field and $\textit{p}$ an odd prime. We prove an automorphy lifting theorem for geometric representations $\rho$ : $\textit{G}_F$ → GL$_2$($\bar{\Bbb Q}_p$) which lift irreducible residual ...
Envelopes of positive metrics with prescribed singularities
(Université Paul Sabatier, ToulouseAnnales de la Faculté des Sciences de Toulouse, 2016)
We investigate envelopes of positive metrics with a prescribed singularity type. First we generalise work of Berman to this setting, proving C$^{1,1}$ regularity of such envelopes, showing their Monge-Ampère measure is ...
On the rigid cohomology of certain Shimura varieties.
(SpringerResearch in the Mathematical Sciences, 2016)
We construct the compatible system of $\textit{l}$-adic representations associated to a regular algebraic cuspidal automorphic representation of GL$_{n}$ over a CM (or totally real) field and check local-global compatibility ...
On the $\phi$-Selmer groups of the elliptic curves y$^2$ = x$^3$ - Dx
(Cambridge University PressMathematical Proceedings of the Cambridge Philosophical Society, 2016-09-09)
We study the variation of the $\phi$-Selmer groups of the elliptic curves y$^2$ = x$^3$ − Dx under quartic twists by square-free integers. We obtain a complete description of the distribution of the size of this group when ...
The augmented base locus of real divisors over arbitrary fields
(SpringerMathematische Annalen, 2016-07-08)
We show that the augmented base locus coincides with the exceptional locus (i.e., null locus) for any nef $\Bbb R$-Cartier divisor on any scheme projective over a field (of any characteristic). Next we prove a semi-ampleness ...
Efficient advert assignment
(InformsOperations Research, 2016-07-01)
We develop a framework for the analysis of large-scale ad auctions where adverts are assigned over a continuum of search types. For this pay-per-click market, we provide an efficient mechanism that maximizes social welfare. ...
The stress–pressure relationship in simulations of MRI-induced turbulence
(Oxford University PressMonthly Notices of the Royal Astronomical Society, 2016-01-01)
We determine how MRI (magnetorotational instability)-turbulent stresses depend on gas pressure via a suite of unstratified shearing box simulations. Earlier numerical work reported only a very weak dependence at best, ...
Growth of eccentric modes in disc–planet interactions
(Oxford University PressMonthly Notices of the Royal Astronomical Society, 2016-03-07)
We formulate a set of linear equations that describe the behaviour of small eccentricities in a protoplanetary system consisting of a gaseous disc and a planet. Eccentricity propagates through the disc by means of pressure ...
Destruction of large-scale magnetic field in nonlinear simulations of the shear dynamo
(Oxford University PressMonthly Notices of the Royal Astronomical Society, 2016-03-03)
The Sun's magnetic field exhibits coherence in space and time on much larger scales than the turbulent convection that ultimately powers the dynamo. In the past the α-effect (mean-field) concept has been used to model the ...