Speaker: German Lugones Instituto de Astronomia, Geofisica e Ciencias Atmosfericas (Sao Paulo, Brazil) ``Quark matter, supernovae and gamma ray bursts'' Although more than three decades of theoretical research and hard numerical modeling have been invested, the mechanism that causes the explosion of massive stars is still not completely understood. This suggests missing physics, possibly related with a transition to quark phases during the deleptonization phase of proto-neutron stars. In the first part of the seminar a brief review of the present status of the standard model of core collapse supernovae and protoneutron star formation is presented. Then we discuss some properties of matter at very high densities, the transition to deconfined quark phases in supernovae and protoneutron stars, the effects of the transition in the explosion mechanism, and the possible production of gamma ray bursts. An interesting feature of the transition is that the influence of the magnetic field expected to be present in neutron star interiors has a dramatic effect on the propagation of the combustion front, generating a strong acceleration of the flame in the polar direction. This results in a (transitory) strong asymmetry in the geometry of the just formed core of hot quark matter. This geometrical asymmetry gives rise to a bipolar emission of the thermal neutrino-antineutrino pairs produced in the process of quark matter formation. Further annihilation into electron-positron pairs just above the polar caps, gives rise to a relativistic fireball, thus providing a suitable explanation for the inner engine of short gamma ray bursts.