PhD at Michigan State

From 2016 to 2021, I was a PhD student at Michigan State University. My advisors were Mark Iwen and Ben Schmidt. You can see my thesis here.

My research focused on reducing the ambient dimension of a manifold object embedded in a Euclidean space with a large dimension without distorting the object too much. One of the motivations for this research is the current prevalence of big data. Often when data is collected, one attempts to collect as much as possible. This can lead to large and bloated data sets that need cleaning later and naturally leads to the idea of dimension reduction.

I proved 2 bounds for such a dimension reduction. One bound was a guarantee that under some circumstances one can achieve a particular reduction. The second was a lower bound, showing that one can not go lower that a particular dimension.

You can see my papers at my Google Scholar profile.