Applications of Algebraic Geometry to Coding Theory, Physics and Computation

Vector bundles on singular projective curves.- On double planes with Kodaira dimension zero.- Computing minimal generators of ideals of elliptic curves.- The Segre and Harbourne-Hirschowitz conjectures.- Pillow degenerations of K3 surfaces.- Computational algebraic geometry today.- Some applications of algebraic curves to computational vision.- Coding theory and algebraic curves over finite fields.- Three algorithms in algebraic geometry, coding theory and singularity theory.- Counting points on Calabi-Yau threefolds.- Subvarieties of abelian varieties.- Characteristic varieties of algebraic curves.- Communication networks and Hilbert modular forms.- Compact Kähler threefolds with small Picard numbers.- Abelian varieties over the field of the 20th roots of unity that have good reduction everywhere.- Using monodromy to decompose solution sets of polynomial systems into irreducible components.- Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry.