The field of Theoretical Computer Science (TCS) is vast and encompasses topics that are the very foundations of computer science. TCS is in the realm of both mathematics and computer science. Historically, it essentially dealt with the questions such as, what do we mean by computation or what is an algorithm? In modern times, the question of efficient computation has become very important and design and analysis of efficient algorithms are at the very heart of computational sciences. The specific topic of computational topology and geometry is about designing efficient algorithms for problems that are of geometric and topological nature. Geometric and topological problems are omnipresent in the scientific world and are very common in our day to day to life as well. For example, computing convex hull of a set of points in plane, clustering a given data in a meaningful way and locating nearest best hospital from one's home. An efficient algorithm that solves these problems and scales to the demand of modern day large and high dimensional data is some of the core problems in the field. The Computer science department at SNU has particular focus on the topic of Topological Data Analysis.
Image Source: Topological Data Analysis