Explore new developments in topological methods for discrete geometry in this 42-minute lecture from the Applied Algebraic Topology Network. Delve into recent applications of the configurations space/test map scheme, focusing on advancements not fully covered in the Handbook of Discrete and Computational Geometry. Discover the emerging field of 'algebraic topology of cooperative games' and its connections to configuration spaces in game theory. Compare these spaces with complexes arising as obstructors for embedding spaces into higher-dimensional Euclidean spaces. Examine a new proof of the 'balanced Van Kampren–Flores theorem' using symmetrized deleted joins and discrete Morse theory, confirming a conjecture by Blagojević, Frick, and Ziegler.