Aldo Cruz-Cota, Ph.D., assistant professor of mathematics, presented his research on the topological complexity of topological surfaces in the 2016 Joint Mathematics Meeting, the largest mathematics meeting in the United States.
"The topological complexity of a surface is an invariant of surfaces that is defined in terms of branched coverings of the Riemann sphere," Cruz-Cota, said. "This invariant measures how efficiently a given Riemann surface can be realized as a branched covering of the Riemann sphere."
The complexity of a surface is a generalization of the concept of hyperbolic area, but the former has the advantage of being well-defined for surfaces of all genera. Cruz-Cota's research focuses on generalizations of the notion of topological complexity of surfaces and their connections to the Hurwitz problem for the existence of branched coverings of the Riemann sphere.
Cruz-Cota also served as a judge and a mentor to the undergraduate students that presented a poster at the 2016 Joint Mathematics Meeting.