Atiyah's conjecture on Yang–Mills and loop-space Morse homology

Let $G$ be a compact Lie group and let $P$ be a principal $G$-bundle over a Riemann surface $\Sigma$. Write $\mathcal A(P)$ for the space of connections on $P$, $\mathcal G_0(P)$ for the based gauge group, $\Lambda G$ for the free loop space of $G$, and let $G$ act on $\Lambda G$ by conjugation. Atiyah's conjecture. There exists an isomorphism

$$HM_{\ast}\big(\mathcal A(P)/\mathcal G_0(P)\big)\cong HM_{\ast}\big(\Lambda G/G\big).$$

The conjecture proposes that the Morse homology associated with the Yang–Mills functional on the quotient of the connection space by the based gauge group agrees with the Morse homology of the loop space of the compact Lie group modulo conjugation, extending the correspondence between Yang–Mills critical points and closed geodesics. The supplied text does not state whether this conjecture has been resolved.