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Thursday 15 Dec 2022Number Theory and Algebra Seminar: Integral representation theory and the topology of 2-complexes

Dr John Nicholson - Imperial College

Harrison 203 14:30-16:30

Abstract: In the 1970s, C. T. C. Wall compiled a list of nine problems concerning the topology of 2-dimensional CW-complexes. These problems are often stated as conjectures, but it is widely believed that there exist counterexamples to most (if not all) of them. Whilst counterexamples have been proposed for many of these problems, the major obstacle lies in the development of the algebraic techniques necessary to show they work. Over the last few years, I have been exploring links between these problems and various aspects of integral representation theory such as the classification of stably free Z[G]-modules. This led to a counterexample to one as well as an affirmative answer to another in a special case.


The aim of the talk will be to give a light introduction to this topic and to explain why methods of integral representation theory are central to many problems in (non-simply connected) topology.


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