I work mainly in general topology and set-theoretic topology. General topology might be defined as the study of limit processes in various settings (e.g., metric space, or more abstract spaces) and set-theoretic topology might be defined as part of the foundations of mathematics involving the interaction of modern set-theory (including descriptive set theory), logic and topology, and to a lesser extent, measure theory. Much work has been done on foundation of point-set topology and general topology, but results reach to most areas of topology. Most recently in general tropology I have worked on hyperspaces, and in set-theoretic topology on remainders of Stone-Cech compactifications.
I am interested in large-scale topological invariants of infinite groups. A finitely generated group with a specified generating set carries a natural metric called the word metric. This turns the algebraic object into a geometric one. Since different choices of generating sets yield distinct metrics, the correct approach is to consider all such metrics equivalent and to focus on the topological properties of the space that are invariant of small changes. I am particularly interested in properties relating to large-scale coverings and notions of dimension. I work on asymptotic dimension and related notions as well as G. Yu's property A.
Yu-Min Chung received his Ph.D. in Mathematics from Indiana University Bloomington in 2013 specializing in computational mathematics. His main research focuses are computational topology and applications to data analysis, called Topological Data Analysis. He has been collaborating with researchers from different scientific disciplines, including those from Dartmouth College to investigate ice at the Arctic, and those from Harvard Medical School to study human red blood cells. Chung's other research interest is computational dynamical systems. He and his group developed one of the first algorithms to compute inertial manifolds, an object from dynamical systems. Prior to UNCG, Chung taught previously at the College of William & Mary, University of Kansas, and Indiana University. Chung has also advised undergraduate honor research students, and REU students, and his students have presented their research work in local and national conferences.