Explore a comprehensive lecture on virtual topological invariants of moduli spaces of sheaves on surfaces. Delve into key concepts including the definition of moduli space, ischaemic points, topological Euler number, and modulus basis. Examine the expected dimension and written formulas related to the topic. Investigate two virtual topological concepts and perfect obstruction theory. Gain insights from speaker Lothar GOETTSCHE of ICTP in this in-depth mathematical discussion.