I got my PhD from the University of Pittsburgh in Summer 2014. Click here for my thesis.
Thesis title: Tukey order on sets of compact subsets of topological spaces.
Thesis adviser: Paul Gartside.
My primary research concerns Analytic Topology and its connections with Foundations and Analysis. Primary focus of my research is the study of the Tukey order, a fundamental notion in order theory, in connection with partially ordered sets arising from topological spaces and the application of the results to key problems in Topology and Analysis. I am also interested in Continuum Theory and have investigated various strengthenings of arc-connectedness property.
Research papers:
Thesis title: Tukey order on sets of compact subsets of topological spaces.
Thesis adviser: Paul Gartside.
My primary research concerns Analytic Topology and its connections with Foundations and Analysis. Primary focus of my research is the study of the Tukey order, a fundamental notion in order theory, in connection with partially ordered sets arising from topological spaces and the application of the results to key problems in Topology and Analysis. I am also interested in Continuum Theory and have investigated various strengthenings of arc-connectedness property.
Research papers:
- (with P.M. Gartside and M. Pitz) n-Arc Connected Graphs. Submitted.
- (with P.M. Gartside) Tukey order, calibres and the rationals. Submitted.
- (with P.M. Gartside) Tukey order and subsets of omega_1. Order. 35 (2018), Issue 1, pp 139–155.
- (with P.M. Gartside) Tukey order on compact subsets of separable metric spaces. Journal of Symbolic Logic. 81 (2016) No. 1, pp 181–200.
- (with B. Espinoza, P.M. Gartside and M. Kovan-Bakan) Strong arcwise connectedness. Houston Journal of Mathematics. Volume 43 (2017) No. 2, pp 577-610.
- (with B. Espinoza and P.M. Gartside) n-Arc connected spaces. Colloquium Mathematicum. Volume 130 (2013), pp 221-240.