Explore the recent developments in Virasoro constraints for moduli spaces of sheaves in this comprehensive lecture by Miguel Moreira from ETH. Delve into the rich history of Virasoro constraints for Gromov-Witten invariants and their evolution in sheaf theory. Discover the general conjecture of Virasoro constraints for moduli spaces of sheaves, formulated using D. Joyce's vertex algebra framework. Learn about the joint work with A. Bojko and W. Lim, which demonstrates the compatibility between wall-crossing and the constraints. Examine the proof of these constraints for moduli of stable sheaves on curves and surfaces with h^{0,1}=h^{0,2}=0. Gain valuable insights into this advanced topic in algebraic geometry and sheaf theory through this in-depth M-Seminar presentation at Kansas State University.