Asteroseismology is the study of the fundamental properties and interior of structure of stars by measuring their oscillations. In cool stars like our Sun, these oscillations are driven by turbulent convection on the surface. Some introductory papers into asteroseismology of cool stars are here, here and here.
The space-based telescopes CoRoT and Kepler revolutionized asteroseismology over the past decade by increasing the number of stars with detected oscillations by almost an order of magnitude over ground-based efforts. This new era of "ensemble asteroseismology" has enabled us to study oscillations in stars ranging from the main-sequence to the tip of the red giant branch. My research group is involved in asteroseismic studies using a variety of datasets, including Kepler, K2 and the recently launched TESS Mission. We are also exploring the potential of data from ground-based transient surveys such as ATLAS and ASAS-SN.
The plot on the right (from Huber 2016) show stars with detected oscillations in a Hertzsprung-Russel diagram. Symbols in the small inset plot on the bottom right show all detections using ground-based observing campaigns prior to the launch of CoRoT and Kepler, illustrating the revolution that these instruments have brought to the field. I developed an automated asteroseismic detection pipeline and led papers studying relations between oscillation frequencies and amplitudes for thousands of red-giants as well as hundreds of dwarf and subdwarf stars observed by Kepler. Such relations are important to understand the driving mechanism for oscillations in low-mass stars, which is related to poorly understood physics of convection. I have also been heavily involved in studies of the core properties of red giant stars through the measurement of gravity-mode period spacings.