r-th roots: better negative than positive

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• Nitin Chidambaram, University of Edinburgh
• Tuesday 25 October 2022, 16:00-17:30
• Lecture Theatre C, Watson Building.

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

I will talk about the construction and properties of a cohomological field theory (without a flat unit) that parallels the famous Witten r-spin class. In particular, one can view it as the negative r analogue of the Witten r-spin class. For r=2, it was constructed by Norbury in 2017 and called the Theta class, and we generalize this construction to any r. By studying certain deformations of this class, we prove relations in the tautological ring, and in the special case of r=2 they reduce to relations involving only Kappa classes (which were recently conjectured by Norbury-Kazarian). In the second part of this talk, we will exploit the relation between cohomological field theories and the Eynard-Orantin topological recursion to prove W-algebra constraints satisfied by the descendant potential of the class. Furthermore, we conjecture that this descendant potential is the r-BGW tau function of the r-KdV hierarchy, and prove it for r=2 (thus proving a conjecture of Norbury) and r=3. This is based on joint work with Elba Garcia-Failde and Alessandro Giacchetto.

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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