Dr. Eduardo Martínez-Pedroza
Research
The principal theme of my research program is the theory of countable infinite groups and its applications to geometry and topology. My contributions are part of the program of classifying and understanding the structure of certain classes of discrete groups. I have been particularly interested in fundamental groups of 3-manifolds, and groups admitting actions on negatively curved spaces. More recently, I have also been working on combinatorical games on graphs in relation with coarse geometry. I have also interests in topological data analysis.
Specific topics include hyperbolic groups and relatively hyperbolic groups, Dehn functions, (high dimensional) homological Dehn functions, finiteness properties, small cancellation groups, CAT(0) groups and non-positively curved cubical complexes. Games on infinite graphs and relation to quasi-isometry invariants.
Some of the tools that I use belong to combinatorics, discrete geometry, algebraic topology, low dimensional topology, and hyperbolic geometry.
Since 2012, my research work has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).