## Research

My research is in differential geometry. My dissertation advisor was Professor Guofang Wei at the University of California, Santa Barbara.

In general, I am interested in the relationship between geometry and topology. In particular, I want to know

*how do local geometric quantities (like curvature!) shape the global topological structure of the manifold?*There are many classical theroems addressing this very question. See, for example, the Bonnet-Myers Theorem or Cartan-Hadamard Theorem.

I am currently investigating the fundamental group of smooth metric measure spaces (complete Riemannan manifolds endowed with a weighted measure). The Bakry-Emery Ricci tensor is a natural analogue to Ricci curvature on such spaces. Since Ricci curvature bounded from below gives us information about Riemannian manifolds, we can ask if the Bakry-Emery Ricci tensor bounded from below gives us similar information for smooth metric measure spaces. For more on my current work, please see my paper on the arXiv: Fundamental Groups of Spaces with Bakry-Emery Ricci Tensor Bounded Below.

email: maree (dot) jaramillo (at) uconn (dot) edu

office: Hartford Times Building 302D