For good summaries of the program, please click on the 'Summary' link on the left. Links to the ADS service pages for the summary papers are provided, along with direct access to the paper pdf files, for those who do not have online access to the papers.
Red dwarf (dM-type) stars are small, cool stars that evolve slowly over time. Their masses are generally 0.6 to 0.08 solar masses, and their luminosities can be as low as 1/10,000th that of the Sun. Below a certain mass (~0.3M¤) and surface temperature (~3200K), dM stars are theorized to be "fully convective" - meaning that, through convective motion in the stellar interior, the entire Hydrogen inventory of the star is available for fusion. This relative abundance of fuel, coupled with the slow fusion rates of dM stars because of their low masses, allows them to have extremely long main sequence lifetimes - possibly trillions of years for the coolest and lowest mass dMs. Even hotter, more massive dM stars have main sequence lifetimes far longer than the Sun.
They are also, by far, the most numerous stars in the local neighborhood and, most likely, in the entire Milky Way, making up >75% of local main sequence stars. Their abundance and long main sequence lifetimes have made them favorable targets to search for planetary companions.
This is part of the motivation for the "Living with a Red Dwarf" program. If there are terrestrial planets orbiting a large number of dM stars, then we must characterize the radiative environments these planets would be subject to as their host star evolves. This will tell us what the likelihood is that complex molecules can form, and whether life can evolve.
dM stars, aside from their numbers and long lifetimes, have many characteristics which would make them interesting hosts for terrestrial planets. For life (as we know it) to exist, a planet must orbit in what is called the "Liquid Water Habitable Zone" or HZ hereafter. This is the distance from the host star where a planet will be of sufficient warmth for liquid water to form without entirely vaporizing or freezing. The Earth is comfortably within the Sun's HZ, as evidenced by our abundance of liquid water. However, a dM star is many times less luminous than the Sun. For this reason, the HZ of a dM star is shrunken.