Your main research interests lie in Lyman-break galaxies.
You are the best, and you know it. Every one of you gets more 8-m class telescope time than the whole of Australia combined. You lead the world: you have the smartest faculty, the hardest working students, the biggest telescopes, and the smoggiest atmosphere. How irritating that all these lesser minds from other, low-grade institutions, get to vote on which facilities should be funded: by rights, the choice should be yours alone!
Until a few year ago, almost no galaxies had ever been found in the high redshift universe. You changed all that: you pioneered the Lyman-break technique, which finds galaxies by searching for the break in their spectra caused by Ly-limit absorption. You take a series of broad-band images: say U, B and R. Galaxies that show up as blue in B and R but are very faint in U will be the ones which have the Ly-limit at around 4000Å: ie. redshift 3 galaxies. With the two Keck telescopes for follow-up spectroscopy, you have identified several hundred galaxies between redshifts 2 and 4. This technique only finds young, dust-free galaxies, but what other sorts of galaxies would you expect in the early universe?
These galaxies (when observed with the Hubble Space telescope) appear as tiny blue specks. Their spectra show that they are young, compact blue galaxies, forming stars at rates of a few solar masses per year. You are finding many of these galaxies per square arcmin: they appear to simply be normal galaxies in the early universe.
What are these galaxies? You hypothesise that they are the ancestors of the bulges of normal spiral galaxies today. These galaxies seem to be forming slowly and steadily: not in single monumental bursts, as some people once thought.
In collaboration with those moderately intelligent people at Lick Observatory and the Space Telescope Science Institute, you used the Hubble Space Telescope observations to extend this technique to fainter galaxies and different redshifts. The Hubble Deep Field (an enormously long pointing at a blank bit of sky) allowed you to find Ly-limit galaxies at redshifts ranging from 1-6. Keck spectra confirmed the redshifts of the brightest galaxies. Piero Madau used your data to calculate the star formation rate of the universe as a function of redshift: he found that it peaks at redshift 1, declining slowly on either side of this redshift.
You are now busily measuring the clustering of these galaxies. They seem to be remarkably strongly clustered. You hope to use this clustering to constrain the geometry of the universe and the nature of dark matter.