[Topology.beta] Tomorrow Samuel and Lauran

[Rot, T.O. (Thomas)]

Dear all,

Samuel and Lauran are going to speak on

Foliations and equivariant diffeomorphism groups [Chap. 2, Ban]

This Friday we have a DDT&G in Leiden.

As I’m traveling I won’t make it to both events, but I wish you good times!

Best,
Thomas

31-10-2025: 14:30-17:00 Leiden, Gorlaeus Building, room BW.0.20 Martijn Kool <https://webspace.science.uu.nl/~kool0009/> : Isotropic Hopf index for orthogonal bundles and Magnificent Four

Abstract: The Hopf index (or Brouwer degree) of a smooth section of a smooth vector bundle plays a fundamental role in topology. When the section and vector bundle are holomorphic, it serves as a model for invariants in enumerative geometry such as Donaldson-Thomas invariants of Calabi-Yau 3-folds.
In part 1 (introductory), I introduce a Hopf-type index of a holomorphic isotropic section of a holomorphic orthogonal vector bundle, and discuss its various characterizations. It serves as a model for Donaldson-Thomas invariants of Calabi-Yau 4-folds. Joint work with Oh-Rennemo-Thomas.
In part 2 (more advanced), I will illustrate its use in the simplest possible counting problem on Calabi-Yau 4-folds: points on C^4. In this case, the (equivariant) isotropic Hopf index can be used to prove a formula discovered in supersymmetric Yang-Mills theory on C^4 by Nekrasov-Piazzalunga. Joint work Rennemo.


-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://listserver.vu.nl/pipermail/topology.beta/attachments/20251027/9eb97b60/attachment.html>