In conclusion, I'd like to enumerate a few questions regarding the chemical evolution of galaxies that seem to need further investigation.
For abundance work in ionized nebulae, we need to understand better the effects of dust on the thermal and ionization balance. The calculated ionizing spectra from massive stars are still in a state of flux, as more physics and opacity are included; this is an area that will continue to require attention as computing power grows. The effects of inhomogeneous structure on the observed emission-line spectrum of H II regions also needs to be addressed.
Stellar nucleosynthesis also needs continuing attention. The biggest remaining problem in theoretical stellar evolution and nucleosynthesis continues to be the treatment of convective mixing, which affects both structure and nucleosynthesis. This is also a hydrodynamical problem requiring improved computing power, and should provide a source of entertainment (and argument) for some time.
We are seeing great improvements in the study of abundances in nearby galaxies, particularly with the new space-based UV and IR observatories, which are greatly improving the data for elements besides oxygen. With these new data, we are in a better position to connect the present-day abundance patterns in galaxies with those observed in high-redshift gas clouds. Eventually, emission-line spectroscopy of distant galaxies should greatly expand our information on heavy element abundances at early times, and allow us to trace the evolution of metallicity in the universe in greater detail. This will be an important complement to the absorption line work on DLAs, as the connection between the emission-line gas and the stellar component is much more clear, and the disk component can be sampled more completely than with absorption studies.
For nearby galaxies one challenge for observers is to compile a homogeneous reference set of abundance data, to provide a statisically significant sample for outlining the relationships between abundances, galaxy mass, and Hubble type, and for understanding the effects of environment on abundance profiles. Some Hubble types are poorly represented in the database, particularly very early Hubble types (Sa-Sab), and very late types (Sd). Basic structural data for nearby galaxies also need improvement. The amount and distribution of molecular gas is one area for improvement. Stellar mass-to-light ratios and the stellar mass surface density distribution is another. Wide-field imaging in the infrared should help reduce the uncertainty in the mass of the stellar component.
One might have noticed that many of the theoretical questions mentioned above come down to hydrodynamics. Understanding star formation, the evolution of galaxies, and the structure of stars all involve hydrodynamics at fundamental levels, so I believe that improved hydrodynamical modeling of all of these phenomena will be the key to a better understanding of galaxy evolution. Understanding the mechanisms which connect abundances in galaxies to galaxy structure should provide a continuing challenge to galaxy evolution theorists.
I am grateful to the organizers of this Winter School for the opportunity to meet and interact with the young scientists (on both the galactic and stellar side) whose research papers I have been enjoying in the past couple of years. Special thanks go to Eric Bell for producing Figure 5 for me, and for informative discussions of the properties of galaxy colors and population synthesis models. The review presented here has also benefitted by numerous conversations over the past years with Daniela Calzetti, Mike Edmunds, Gary Ferland, Claus Leitherer, John Mathis, Andy McWilliam, and Verne Smith. Finally, I must also acknowledge my various collaborators on galaxy abundances (Reginald Dufour, Rob Kennicutt, Greg Shields, Evan Skillman, Manuel Peimbert, and Silvia Torres-Peimbert) who have contributed greatly to many of the results I have presented in these lectures. My work on abundances in galaxies has been supported the past four years by NASA grant NAG5-7734.