Normal forms for logarithmic flat connections

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• Francis Bischoff (Oxford)
• Tuesday 18 October 2022, 16:00-17:30
• Lecture Theatre C, Watson Building.

If you have a question about this talk, please contact Tyler Kelly.

In the pre-talk I will review the Riemann-Hilbert correspondence from the perspective of Lie groupoids, where it can be viewed as an instance of Lie’s second theorem. For the talk, I will discuss my recent preprint (arXiv:2209.00631) on the classification of flat connections on C^n with logarithmic singularities along a weighted homogeneous hypersurface. In this work, I apply Lie theoretic techniques to obtain normal form theorems for these connections. In the simplest case, this gives a new proof of the known classification of ODEs with Fuchsian singularities. An upshot of this work is an explicit description of the moduli space of log connections as an algebraic quotient stack. I will end by describing these spaces and discussing ongoing work on studying their geometry.

This talk is part of the Geometry and Mathematical Physics seminar series.

This talk is included in these lists:

• Bham Talks
• Geometry and Mathematical Physics seminar
• Lecture Theatre C, Watson Building
• School of Mathematics Events

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