Topology is the mathematical theory of the "shape of spaces". It gives a flexible framework in which the fabric of space is like rubber and thus enables the study of the general shape of a space. The spaces often arise indirectly: as the solution space of a set of equations; as the parameter space for a family of objects; as a point cloud from a data set; and so on. This leads to strong interactions between topology and a plethora of mathematical and scientific areas. The love of the study and use of topology is far reaching, including the use of topological techniques in the phases of matter and transition which received the 2016 Nobel Prize in Physics. This unit introduces you to a selection of topics in pure or applied topology. Topology receives strength from its areas of applications and imparts insights in return. A wide spectrum of methods is used, dividing topology into the areas of algebraic, computational, differential, geometric and set-theoretic topology. You will learn the methods, key results, and role in current mathematics of at least one of these areas, and gain an understanding of current research problems and open conjectures in the field.
4-5 contact hours/week comprising lectures, and tutorials or seminars
tutorial participation (10%), written assignments (40%), final exam (50%)
Familiarity with metric spaces (e.g., MATH4061 or equivalent) and algebraic topology (e.g., MATH4311 or equivalent). Please consult with the coordinator for further information.