SU(n)–Casson invariants and symplectic geometry

In 1985, Casson introduced an invariant of integer homology 3-spheres by counting SU(2)SU(2)-representations of the fundamental groups. The generalization of Casson invariant by considering Lie groups SU(n) has been long expected, but the original construction of Casson encounters some difficulties. I will present a solution to this problem, highlighting the equivariant symplectic geometry and Atiyah-Floer type result entering the construction.