Abstract: J. Craig Wheeler (Wednesday April 15, 3:00 PM) Deep Supernovae: Lambda or Not? Searches for deep supernovae of Type Ia at redshift of 1/2 to 1 are beginning to pay off in spectacular fashion. The early results show that deep supernovae are systematically a little fainter (by about 0.3 magnitudes) than the nearby sample. This result is suggestive of a low value of the mean matter density and a positive value of the cosmological constant. The key question emerging from this area is the evaluation of systematic effects that could amplify or negate the effect. Topics such as progenitor evolution, galactic radial distribution, polarization that suggests angular variation in the luminosity and variations in the reddening law, and the physics of thermonuclear combustion will be discussed. Subtle differences can be sorted out with detailed, well time-sampled spectral evolution and deeper understanding of the physics of the explosion. The payoff will be better understanding of supernova progenitor evolution, explosion physics, the history of star formation, and galaxy evolution.