Joshua Cruz, Graduate Student
I am a graduate student of Les Saper. For my thesis, I have been calculating L^{2} cohomology groups of incomplete metrics coming from singular complex varieties. This work is an interesting example of the interplay between analysis and topology.
I have done work in several other fields as well, including mathematical neuroscience, applied sheaf theory, and applied topology more broadly. Please note: Joshua has left the Mathematics department at Duke University; some info here might not be up to date.  Contact Info:
Office Location:  274G Physics  Email Address:    Office Hours:
 Help Room Hours: Monday 68pm in Carr 132
 Education:
BS  Washington State University  2013 
 Research Interests:
Current projects:
Some Results on Max IntersectionComplete Codes, Decomposing Vineyards with Sheaf Theory
I am a student of Les Saper, with broad interests in algebraic topology and complex geometry.
I am also interested in many other fields of mathematics, including geometric analysis, functional analysis, representation theory, stochastic analysis, and applied topology, especially persistent homology.
 Keywords:
Applied Topology • Probability theory and stochastic processes • Sheaf theory • Topology
 Recent Publications
 Cruz, J; Giusti, C; Itskov, V; Kronholm, B, On Open and Closed Convex Codes,
Discrete & Computational Geometry, vol. 61 no. 2
(March, 2019),
pp. 247270, Springer Science and Business Media LLC [doi]
