Program: - The morning talks will consist of two short courses devoted to two themes. - The first is an introduction to the notions and basic results of lattices and sphere packings. In particular, we discuss packing and covering invariants, connections with codes, theta functions, and ideal lattices. - The second is an introduction to the theory of Arakelov class groups of number fields. We study the ideal lattices associated to Arakelov divisors and the notion of a reduced Arakelov divisor. We discuss the analogy with the theory of algebraic curves over finite fields. We also pay attention to computational applications, such as Buchmann's algorithm

Schedule: - Two instructional talks in the morning: 9.45-10.45, 11.00-12.00. - Two or three talks in the afternoon: 16.30-19:00 - Wednesday Morning three talks 9.00-12.30, with free afternoon. Monday 2   9.45-10.45  Baran, Arakelov class groups 11.00-12.00  Suarez, Lattices 16.30-17.30  Mihăilescu, On cyclic Lambda-modules in Zp-extensions of number fields 17.45-18.15  Picone, Automorphisms of Hyperelliptic GAG-codes 18.30-19.00  Brakenhoff, Class semi-groups for general orders Tuesday 3   9.45-10.45  Suarez, Lattices 11.00-12.00  Baran, Arakelov class groups 16.30-17.30  Thomas, Normal basis generators in p-extensions of local fields 17.45-18.15  Nuccio, Cyclotomic units and class groups 18.30-19.00  Verhoek, Group schemes of order 4 Wednesday 4   9.00-10.00  Dassen, The LLL-algorithm 10.15-11.00  Baran, Arakelov class groups 11.15-12.15  Schoof, Odlyzko's discriminant bounds Thursday 5   9.45-10.45  Baran, Arakelov class groups 11.00-12.00  Suarez, Lattices 16.30-17.30  Rühl, Annihilating Polynomials of Excellent Quadratic Forms 18.00-19.00  Palenstijn, Entanglement and Artin's primitive root conjecture Friday 6   9.45-10.45  Suarez, Lattices 11.00-12.00  Schoof, Buchmann's algorithm 16.30-17.30  Stevenhagen, Complex multiplication in low genus 18.00-19:00  Streng, Class polynomials in genus 2