Geometry and Topology

Topology is the study of shape of objects, and considers what quantities change or do not change when an object is changed in a continuous manner. Geometry studies notions such as distance, area, volume and also curvature which is another measure of shape, and there are spectacular connections between geometry and topology. The area uses techniques from algebra and analysis, and has connections with many other areas of pure mathematics, applied mathematics and and mathematical physics. The research group in MSCS has particular interests in differential geometry, complex geometry, geometric group theory, geometric topology and the study of Higgs bundles.