ar X iv : a st ro - p h / 99 09 09 6 v 1 5 S ep 1 99 9 Conference

There are hints that nearby Type Ia supernovae may be a little different than those at large redshift. Confidence in the conclusion that there is a cosmological constant and an accelerating Universe thus still requires the hard work of sorting out potential systematic effects. Polarization data show that core-collapse supernovae (Type II and Ib/c) probably depart strongly from spherical symmetry. Evidence for exceedingly energetic supernovae must be considered self-consistently with evidence that they are asymmetric, a condition that affects energy estimates. Jets arising near the compact object can produce such asymmetries. There is growing conviction that gamma-ray bursts intrinsically involve collimated or jet-like flow and hence that they are also strongly asymmetric. SN 1998bw is a potential rosetta stone that will help to sort out the physics of explosive events. Are events like SN 1998bw more closely related to " ordinary " supernovae or " hypernovae? " Do they leave behind neutron stars as " ordinary " pulsars or " magnetars " or is the remnant a black hole? Are any of these events associated with classic cosmic gamma-ray bursts as suggested by the supernova-like modulation of the afterglows of GRB 970228, GRB 980326 and GRB 990712? New data is driving both supernova and γ-ray burst research and suggesting that these subjects may be related. A central issue in both areas is the breaking of spherical symmetry. This conference celebrated as much as any single thing the emergence of evidence and argument for strong breakdown of spherical symmetry for both supernovae and γ-ray bursts and especially the resulting potential for links between them, whether those links are supernovae or " hypernovae. " Supernova studies have also revolutionized the study of cosmology. There spherical symmetry is not at issue, but the prospect of an accelerating Universe presents many challenges. I cannot synthesize all the energetic work presented in oral talks and poster presentations , never mind over coffee and dinner, at this symposium that mixed two " exploding " fields. I will attempt to give a summary of certain highlights and connective themes that I think will set the course for future research. In §2, I give a brief summary of the exciting work on SN Ia, their associated physics, and their application to cosmology. Some perspectives on γ-ray bursts and their possible link to supernovae or " hypernovae " are presented in §3. New results on the propagation of a …