**Otis Chodosh, Stanford University **

**Title:**
Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions

**Abstract:** I will discuss joint work with C. Li and
Y. Liokumovich in which we classify (up to homotopy) 4 dimensional
compact manifolds with π_{2} = 0 that admit Riemannian metrics of
positive scalar curvature. Namely, after passing to a finite cover,
such a manifold is homotopy equivalent to S^{4} or a connect sum of S^{3}
x S^{1}'s. (The analogous statement holds for 5-dimensional manifolds
with π_{2} =π_{3} =0).