I’m RM Causey, and I’m an instructor at Miami University.
I earned a B.S. in math at Mississippi State University in 2009 and a Ph.D. in math from Texas A&M University in 2014. My primary research interests are Ramsey theory, functional analysis, greedy approximations, and local theory. More precisely, I enjoy using Ramsey theory, ordinal indices, descriptive set theory, and non-linear metric theory to classify linear operators between Banach spaces.
The large-scale structure of my research has been concerned with using transfinite methods to delineate and investigate operators ideals, operator factorization, and renorming theorems. In particular, I use ordinal indices (notably the Szlenk index, dentability index, Bourgain index, and James index) and non-linear transfinite metric structures to define and study classes of operators.
I also greatly enjoy teaching and working with students. In the past, I have led a graduate student seminar concerning the intersection of Ramsey theory and Banach space theory. Several of my research problems have yielded combinatorial and topological questions which are easily accessible to graduate and advanced undergraduate students. My goal is to invite students to more advanced mathematical research by guiding them through these research projects.