Background:At its core, much of mathematics is concerned with the problem of classifying mathematical structures. Often, one cannot solve the classification problem by simply listing mathematical structures of a given type, as there are continuously varying parameters that enter into the description of the mathematical structures involved. In such cases, the space over which the parameters vary can often be constituted into a ‘geometrical structure’ called a moduli space for the classification problem at hand. On the one hand, understanding the ‘shape’ of this moduli space is tantamount to ‘solving’ the original classification problem, while on the other hand, moduli spaces provide a rich source of examples of interesting geometrical structures whose study is of intrinsic interest.In geometry and topology, vector bundles – families of vector spaces that are parametrized by a space – play a central role. The study of moduli spaces of vector bundles, and closely related structures such a...
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