# Colloquium abstracts

**Anusha Mangala Krishnan**

Syracuse University, USA

February 25, 2021

**Prescribing Ricci curvature on a product of spheres**: The Ricci curvature Ric(g) is a symmetric 2-tensor on a Riemannian manifold (M,g) that encodes curvature information. The Ricci curvature features in several interesting geometric PDEs such as the Ricci flow and the Einstein equation. The nature of Ric(g) as a differential operator in particular its nonlinearity and the fact that it is degenerate make these PDEs particularly challenging. In this talk I will address the following question. Given a symmetric 2-tensor T on a manifold M, does there exist a metric g such that Ric(g) = T? I will discuss some classical results as well as some recent work in the presence of symmetry.