Presentation #102.03 in the session Dynamics Beyond the Main Sequence.
The evolution and stability of planetary system architectures, key to planetary habitability, remains poorly understood. Both interactions between neighboring planets as well as between the planets and their host star can sculpt planetary systems on long (> Gyr) timescales. Characterizing the planet population of post-main sequence stars can reveal the relative strength and frequency of these interactions, playing a crucial role in helping us to understand the past, present and future of planetary systems. Here we introduce the planets discovered so far as part of the TESS Giants Transiting Giants program. With star and planet mass and radius constraints, we constrain the rate and efficiency of star-planet and planet-planet interactions in these systems. We find that planets transiting evolved stars display a wide range of inflation rates, and appear to follow a generally monotonic period-eccentricity relation, where longer-period planets appear to have higher eccentricities. We compare this population to the long-period, non-transiting population of evolved planetary systems and binary stars, and demonstrate how future observations of evolved systems can bridge gaps in our understanding of the evolution and longevity of planetary systems.