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The homology of configuration-section spaces

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Martin Palmer-Anghel || GER
Mathematical Institute of the Romanian Academy, Bucharest
Tue, 28/06/2022 - 11:45 - 12:15
Configuration-section spaces parametrise fields with singularities on a given manifold, and may be viewed as an enrichment of configuration spaces by non-local data. Hurwitz spaces are two-dimensional examples of these, parametrising branched coverings of surfaces, and the behaviour of their homology is important for questions in analytic number theory, as shown in a celebrated result of Ellenberg, Venkatesh and Westerland on the Cohen-Lenstra conjecture. I will talk about joint work with Ulrike Tillmann (some published and some in progress) on homological stability and the stable homology of configuration-section spaces. Time permitting, I will also explain how similar techniques may be applied to asymptotic monopole moduli spaces.


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