Joshua Cruz, Graduate Student

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. 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 6-8pm in Carr 132

Education:

BS

Washington State University

2013

Research Interests:

Current projects: Some Results on Max Intersection-Complete 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

1. Cruz, J; Giusti, C; Itskov, V; Kronholm, B, On Open and Closed Convex Codes, Discrete & Computational Geometry, vol. 61 no. 2 (March, 2019), pp. 247-270, Springer Science and Business Media LLC [doi]