This workshop is the first annual meeting of the Marie Curie ResearchTraining Network <a href="http://websites.math.leidenuniv.nl/gtem"
;>GaloisTheory and Explicit Methods</a>. This project funds 12 PhD students indifferent places in Europe in a collaborative research project in thearea of explict methods in number theory and arithmic geometry. The goal of the present meeting is to expore new scientific ideas anddirections in the network's key areas: lattices and Arakelov theory,Galois representations, constructive Galois theory and effectivecohomology computations. In particular the meeting will review theresearch of the passed year, look ahead to the next year, and seek new input from experts outside the network. In addition, the workshop will have a tutorial component in the specificspecific subject of function fields (intended topics: Riemann Roch,Riemann hypothesis, analogy with number fields). The workshop participants will be a mix of senior research staff andPhD students both from inside (2/3) and outside (1/3) the network.