Global Parton Distributions for the LHC Run II

We review the next generation global PDF sets: NNPDF3.0, MMHT14 and CT14. We describe the global datasets, particularly the new data from LHC Run 1, recent developments in QCD theory and PDF methodology, improvements in combination and delivery, and future prospects for parton determination at Run 2.Comment: 15 pages, 11 figures; talk given at La Thuile, 3rd March 2015; updated reference

High Energy Resummation of Drell-Yan Processes

We present a computation of the inclusive Drell-Yan production cross-section in perturbative QCD to all orders in the limit of high partonic centre-of-mass energy. We compare our results to the fixed order NLO and NNLO results in MSbar scheme, and provide predictions at NNNLO and beyond. Our expressions may be used to obtain fully resummed results for the inclusive cross-section.Comment: 18 pages, 5 figures: version to be published in NP

Unital hyperarchimedean vector lattices

We prove that the category of unital hyperarchimedean vector lattices is equivalent to the category of Boolean algebras. The key result needed to establish the equivalence is that, via the Yosida representation, such a vector lattice is naturally isomorphic to the vector lattice of all locally constant real-valued continuous functions on a Boolean (=compact Hausdorff totally disconnected) space. We give two applications of our main result.Comment: 15 pages. Submitted pape

Momentum Conservation at Small x

We discuss how momentum conservation is implemented in perturbative computations based on expansions of anomalous dimensions appropriate at small $x$. We show that for any given choice of $F_2$ coefficient functions there always exists a factorization scheme where the gluon is defined in such a way that momentum is conserved at next to leading order.Comment: 11 pages, plain TeX with harvma

An Improved Splitting Function for Small x Evolution

We summarize our recent result for a splitting function for small x evolution which includes resummed small x logarithms deduced from the leading order BFKL equation with the inclusion of running coupling effects. We compare this improved splitting function with alternative approaches.Comment: 5 pages, 2 figures, presented by G.A.at DIS200

Double Asymptotic Scaling '96

We review recent HERA data on the structure function F_2 at small x and large Q^2. We show that the salient features of the data are revealed by comparing them to the double asymptotic scaling behaviour which F_2 is predicted to satisfy in perturbative QCD.Comment: 5 pages, LaTeX with espcrc2.sty (included), 11 figures included by epsfi