Analytic Torsion and Reidemeister Torsion

We announce a proof of the conjecture of Ray and Singer that for a compact Riemannian manifold the analytic torsion and Reidemeister torsion are equal. The proof involves studying the heat equation for certain manifolds M, equipped with metrics g_u, 0 < u < 1 which degenerate in a prescribed way at the boundary δM, as u → 0,1.