  Driven largely by multiple ground-based radial-velocity (RV) surveys and
photometric space missions such as Kepler and K2, the discovery of new
exoplanets has increased rapidly since the early 2000s. However, due to a
target selection bias in favor of main-sequence stars, only a handful of
transiting planets have been found orbiting evolved hosts. These planets, most
of which are giants, hold important information regarding the formation and
evolution of planetary systems. In this thesis, I sought to increase the sample
of known giant planets orbiting red-giant stars, focusing on data from NASA's
Transiting Exoplanet Survey Satellite (TESS) mission, and to improve their
characterization. Specifically, I focused on close-in giant planets orbiting
(preferably) oscillating low-luminosity red-giant branch (LLRGB) stars. To
improve characterization, I developed a method to model planetary transits and
stellar signals simultaneously, implementing Gaussian processes to model
stellar granulation and the oscillations envelope in the time domain. My
results show that the model enables time-domain asteroseismology, inferring the
frequency of maximum oscillation amplitude, $\nu_\text{max}$, to within 1\%.
The method's implementation is open-source and available to the community.
Regarding the planet search, I assembled a pipeline, mostly comprised of
third-party open-source software and explored a sample of $\sim$40,000 bright
LLRGB stars in the southern hemisphere of TESS's field of view. The search
identified four planet candidates, two of which are not currently known planets
and orbit red-giant stars. Radial-velocity follow-up observations of both these
candidates have tentatively confirmed their planetary nature. Finally, I also
confirmed the planetary nature of an additional candidate, not part of the
above sample, through RV observations.
