Introduction

Hello, all!

This will be my new (professional) blog as I leave graduate school and begin to look for research topics to begin publishing papers.

I have a Ph.D. in differential topology from UWM and am teaching adjunct at Marquette University in Milwaukee, WI. My dissertation is online at the arXiv at this link

My dissertation is pseudo-collars, which are intended to be generalizations of triangulation of Hilbert cube manifolds. Chapman and Siebenmann proved that for aspherical Hilbert cube manifolds that admit Z-compactifications, if they have the same fundamental group, then they are homeomorphic. My dissertation advisor, Craig Guilbaut, along with his co-author Fred Tinsley of Colorado College, seek to prove an analogous result for high-dimensional, but finite dimensional, manifolds. thus proving a long-standing open conjecture called The Borel Conjecture.

So, my dissertation topic is on pseudo-collars, but it's not where my heart is. Honestly, I was just glad Craig was able to find a topic that was in manifold topology and not Geometric Group Theory, which has taken the field of topology research mathematics by storm.

Since I graduated in May, 2015, and wanted to work on a research project, Craig counseled me not to just go after the glory of a "Big Game" conjecture, like The Borel Conjecture, but to work on topics I find "beautiful". (More on that word later.) So, I did quite a bit of soul-searching, and found global analysis and geometric control theory to be topics nearer and more dear to my heart.

So, in a nod to John Baez's "This Week's Finds in Mathematics Physics", I started this blog, mainly as a place for me to think out out loud on my newfound direction in research, global analysis (differential equations on manifolds and related topics, and geometric control theory). As the title of the blog may partially suggest, I hope that by putting pressure on myself to have to update this blog weekly with new "finds" and information, it will keep me at the grindstone of learning about possible research topics/areas. I hope other people will find it interesting as well.