Explore recent developments in Hermitian Yang-Mills theory for sheaves on mildly singular spaces in this 57-minute lecture by Mihai Paun at BIMSA. Delve into the findings presented in arXiv:2303.08773 and arXiv:2405.10003, focusing on log terminal Kähler spaces. Gain insights into the latest research and advancements in this specialized area of mathematical physics and geometry.