Research Statement Jeong -

My research interests lie in Discrete Mathematics, especially Combinatorics, Graph Theory, Combinatorial Geometry, and Combinatorial Number Theory. For me, the most exciting aspect of working in discrete mathematics is the prevalence of combinatorial problems in various fields of mathematics and various applications to Computer Science and real life problems such as building transmitters in a town, assignment of radio channels, scheduling meetings, etc. Graph theory and combinatorics provide a unifying abstract structure for these problems. At the same time, significant progress in combinatorial problems requires application of tools/methods from a variety of fields like probability, geometry, algebra, number theory, etc. I have experienced both these aspects of research in combinatorics through my work on geometric combinatorial problems and number theoretic combinatorial problems: my proofs employ ideas from discrete Geometry, probability, asymptotic analysis, and number theory. [23, 24, 40]. In the long term, I will continue to deepen and broaden my understanding of fields like geometry, algebra, number theory, and probability, as well as combinatorics, so that I can make contributions across a wide range of topics which lie in the intersection of these fields with combinatorics. In this statement, I will discuss my research and results to date and then briefly describe other topics that I have worked on or intend to in the near future.