Title: Moduli spaces of bundles in low genus and degeneracy loci. Abstract: Coble hypersurfaces enjoy very special properties related to abelian varieties and moduli of semistable bundles of rank r with trivial determinant on a curve C of genus g, notably when (g,r) equal to (2,3) or (3,2). Using orbital degeneracy loci arising from Vinberg theta-groups and Hecke cycles, we describe moduli of semistable bundles with fixed odd determinant as subvarieties of Grassmannians, again when (g,r) equals (2,3) or (3,2). The geometry of these loci and of their singularities parallels that of Coble hypersurfaces and is related to projective models of K3 surfaces of genus 13 and 19. Joint work with Vladimiro Benedetti, Michele Bolognesi, Laurent Manivel.