| Abstract: Every Sun-like star will eventually evolve into a red giant, a transition which can profoundly affect the evolution of a surrounding planetary system. The timescale of dynamical planet evolution and orbital decay has important implications for planetary habitability, as well as post-main sequence star and planet interaction, evolution and internal structure. I am investigating the population of giant planets transiting low luminosity red giant branch stars observed by the NASA K2 and TESS missions. Our team has led the discovery of two new planets orbiting evolved stars, and confirm the existence of a third, doubling the number of evolved (Rstar > 3.5 Rsun, Teff,star < Teff,sun) stars with known transiting planets. By developing new Bayesian tools to mitigate stellar variability in evolved star light curves, I am able to robustly measure the planetary radii of these systems. I find that all of these planets are inflated, the first evidence that planets may be inflated directly by incident stellar radiation rather than by delayed loss of heat from formation, thus comprising a previously unknown class of re-inflated planets. I also obtain radial velocity measurements of planets orbiting evolved stars to constrain their orbital properties and the efficiency of re-inflation. I find that close-in giant planets orbiting evolved stars display a preference for moderately eccentric orbits, a previously predicted effect of tidal circularization and planet inspiral in evolved star planetary systems. Finally, I perform a comprehensive planet occurrence study using all oscillating low luminosity red giant branch stars observed in the first 16 campaigns of K2. I measure stellar masses and radii to 6% precision or better using asteroseismology, and find a comparable fraction of close-in giant planets around evolved stars as main sequence stars. A higher fraction of inflated close-in gas giants is also found around evolved stars. The discovery of these systems implies that planet engulfment happens more slowly than previously predicted, and that the effects of stellar evolution on the occurrence of close-in planets larger than Jupiter is not significant until stars have begun ascending substantially up the red giant branch (~>6 Rsun). Further surveys of these stars by the NASA TESS mission will allow us to understand the dependence of late-stage planetary evolution on star and planet properties. |