Joshua Cruz

Joshua Cruz
  • Student
Office Hours: 

Help Room Hours: Monday 6-8pm in Carr 132

I am a graduate student of Les Saper. For my thesis, I have been calculating L2 cohomology groups of incomplete metrics coming from singular complex varieties. For example, one would like to show that the L2 cohomology of a small neighborhood of an isolated singular point is the cohomology of the link in low degrees and zero in high degrees. This work is an interesting example of the interplay between analysis and topology.

I also work in applied topology. I wrote a paper in 2016 with Chad Giusti, Vladimir Itskov, and Bill Kronwell on convex codes, a concept coming from neuroscience which describe the neural firing patterns of (e.g.) placeholder cells. More recently, I've been working on applied sheaf theory, much of which was in collaboration with Justin Curry.