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- FIELD
- Math: HCMC
- DATE
-
Oct 11 (Fri), 2024
- TIME
- 10:00 ~ 11:00
- PLACE
- ONLINE
- SPEAKER
- Osuga, Kento
- HOST
- Oh, Jaeseong
- INSTITUTE
- University of Tokyo
- TITLE
- [HG_A] b-Hurwitz numbers from Whittaker vectors for W-algebras
- ABSTRACT
- G-weighted Hurwitz numbers can be interpreted as sum of ribbon graphs embedded into orientable surfaces with certain weight G, and G-weighted b-Hurwitz numbers are their non-orientable analogues with the notion of measure of non-orientability proposed by Chapuy-Dolega. It was further observed by Bomzon-Chapuy-Dolega that for (very) simple choices of G, their b-Hurwitz numbers satisfy Virasoro constraints. Then, one may ask: what if we choose G to be a more general form? Do they still satisfy Virasoro constraints or are they related to different algebras? In this talk I will show a nontrivial relation between b-Hurwitz numbers and so-called Whittaker vectors for W-algebras --- a generalisation of the Virasoro algebra. If time permits, I will also discuss how they are related to topological recursion as well as refined topological recursion. This talk is based on joint work with Nitin Chidambaram and Maciej Dolega, and the main reference is arXiv:2401.12814.
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