Alastair Anderberg, The University of Newcastle
Dr David Roberts, The University of Adelaide
Algebraic topology is one of the key areas of pure mathematics to be developed in the middle of the 20th century, with techniques leaking out to many other areas of mathematics aside from its origin in topology. These days it is even showing up in applied mathematics, with topological data analysis becoming a larger field every year. This course aims to give a first treatment of algebraic topology using cohomology, taking both a combinatorial and topological point of view, and treating the basics of homological algebra used to do computations. We will also cover the basic ideas of category theory so as to take advantage of functoriality of cohomology.
This course should be suitable for a first introduction to modern ideas of topology, homological algebra, algebraic topology and the basic language of category theory.
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David is a pure mathematician working at the intersection of category theory and geometry (and other topics). He is currently a postdoc in the Institute for Geometry and its Applications at the University of Adelaide. David’s research largely involves finding the abstract structure behind other parts of mathematics, and also creating new instances of abstract nonsense in as concrete terms as possible.