Who am I?
I am currently finishing my doctoral studies in Geometry under the supervision of Blaine Lawson and Christina Sormani.
My doctoral research is on the metric properties of Euclidean vector bundles (with compatible connections) endowed with Riemannian metrics of Sasaki type on their total spaces. It may be divided in two: a static part and a dynamic part. The former focuses of the interplay of the ambient Sasaki-type metric, the linear structure of the fibers and the action of the holonomy group, while the latter studies the behavior under (pointed) Gromov-Hausdorff limits of said bundles.
A particular feature of these constructions is the assignment, \(L:Hol\rightarrow\mathbb{R}\), given by \[L(a)=\inf_{\gamma}\ \ell(\gamma),\] where \(\gamma \) is a loop generating \(a\in Hol\) by parallel translation. Anything you can tell me about this map —which is not even lower semi-continuous— is very much welcomed!
What I can tell you about it is that it is a group-norm and that its degeneration is responsible for the structure of limiting fibers under a pointed Gromov-Hausdorff convergence. For more info, go to my Research section.
Why are you here?
There are a few possible reasons. One is that you are my student and are wondering how to find me (if so, look around and hopefully you will).
Another possibility is that you are trying to hire me (if so, please stop by my CV and the research section; these may or may not convince you, but it's worth a try).
To mention yet another option (but by no means finishing up the hypothetical list) you might have just found your soul-mate (if so —and under the potentially hazardous assumption that such relation is an equivalence relation, or at least a symmetric one— then I strongly suggest you contact me immediately).
If all of these fail and I haven't been able to answer the question (have you?), please go to the Links section. There might be some interesting escape routes there.