Description: | [DMS Seminar] Dr. Swarnendu Sil (Forschungsinstitut für Mathematik, ETH Zurich) -- Topology of Sobolev $G$-bundles via Coulomb gauges in critical dimension |

Date: | Wednesday, Aug 21, 2019 |

Time: | 3 p.m. - 4 p.m. |

Venue: | G09, A P C Ray |

Details: | The analysis for Yang-Mills functional and in general, problems related to higher dimensional gauge theory, often requires one to work with notions of Sobolev principal bundles and Sobolev connections on them. The bundle transition functions for a Sobolev principal $G$-bundle are not continuous in the critical dimension and thus the usual notion of topology does not make sense. In this talk, we shall see that if a bundle $P$ is equipped with a Sobolev connection $A$, then one can associate a topological isomorphism class to the pair $\left( P, A\right),$ which is invariant under Sobolev gauge changes. In stark contrast to classical notions, this notion of `bundle topology' is \emph{not} independent of the connection. However, for more regular bundles and connections, this coincides with the usual notion. On the other hand, we shall see that this notion behaves well with respect to passage to the limit of sequences with control on $n/2$-Yang-Mills energies and is thus more suitable to capture the change of topology in the limit due to concentration of curvatures. |

Calendar: | Seminar Calendar (entered by sushil.gorai) |

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