### Math at Syracuse University

#### Codimension One Homology of Noncompact Manifolds with Nonnegative m-Bakry Émery Ricci Curvature :

The aim of this talk is to discuss relations between the m-Bakry Émery Ricci curvature and the n-1 integer homology. We will see how this relates to the Cheeger-Gromoll Splitting Theorem, and Sormani's Line Theorem.

Presented at the Virtual Workshop on Ricci and Scalar Curvature Talk

#### Which Locally homogeneous compact 3-manifolds satisfy m-quasi Einstein metrics?

In this talk, we will answer the question, "which locally homogeneous compact 3-manifolds admit m-quasi Einstein metrics?" First, we will define locally homogeneous and m-quasi Einstein. We will use the Bakry Emery Ricci versions of Myers' Theorem and the Splitting Theorem, as well as the Lie structure of well known Lie groups to answer our question. We will also talk about what happens if Lie groups admit m-quasi Einstein metrics.

Presented at the Association for Women in Mathematics poster session