Explore a 55-minute conference talk from the Fields Institute's "Theta Series: Representation Theory, Geometry, and Arithmetic" event, delivered by Luis Garcia from University College London. Delve into recent constructions of Eisenstein cocycles of arithmetic groups, examining their development through equivariant cohomology and differential forms. Discover how these objects function as theta kernels, connecting arithmetic group homology to algebraic structures. Investigate the application of these concepts to Sczech and Colmez's conjectures on critical values of Hecke L-functions. Follow the progression from introduction and explicit examples through modular symbols, abstract frameworks, and equivalent chromology to the exploration of symmetric spaces, differential forms, and fractional ideals.