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Asteroseismology is a young and rapidly developing field in stellar astrophysics. It enables efficient probes of stellar interiors and provides critical input to many fields in contemporary astrophysics. Being very sensitive to the total time span and precision of individual stellar brightness measurements, observational asteroseismology has experienced significant boosts with the launch of space-missions such as CoRoT, Kepler/K2, and TESS. The interior macro- and micro-physics are being probed with unprecedented precision for isolated stars, as well as small- to intermediate-sized stellar populations across the entire HR-diagram. Powerful synergies between asteroseismology and fields such as binary stars, exoplanets, clusters, galactic archeology, etc. are emerging fast. In this joint 6th/13th in a series of TASC/KASC workshops, we aim to put asteroseismology in a wider context, reaching out to other fields in astrophysics, focusing on the above synergies with specific attention to joint exploitation of large-scale space- and ground-based surveys. We will celebrate the 10th anniversary of “Kepler Asteroseismology in Action” started during KASC3 at Aarhus University, where Kepler asteroseismology was put into practice for the first time, opening a new horizon for observational asteroseismology as we know it today. KASC6/TASC13 will highlight the first results emerging from the full-sky, double-hemisphere TESS data exploration, in synergy with other and complementary large-scale surveys. The TASC6/KASC13 workshop will take place from 13-17 July 2020 at KU Leuven, Belgium - one of the most active asteroseismic centers in Europe.