[Topology.beta] FW: DDT&G seminar @Leiden on June 6: Martijn Kool

[Rot, T.O. (Thomas)]

Dear all,

You are cordially invited to attend the next Dutch Differential Topology and Geometry seminar, which will take place next week in Leiden.

Speaker:  Martijn Kool<https://www.uu.nl/medewerkers/MKool1> (Utrecht)
Title: Isotropic Hopf index for orthogonal bundles and Magnificent Four
Date: Friday 6 June, 14:30-17:00
Location: Leiden, Gorlaeus Building, room BW.0.19

The schedule will be as follows:

2:30-3:30 p.m.: first part of the seminar (little to no prior knowledge assumed)
4:00-5:00 p.m.: second part of the seminar (slightly more advanced level)

Please notice that the first part of the seminar (2:30-3:30 p.m.) is intended for general mathematical audience, and master students with an interest in geometry and topology are especially encouraged to participate.

Please visit the seminar's webpage for additional information and an overview of past and upcoming talks:

https://www.few.vu.nl/~trt800/<https://www.few.vu.nl/~trt800/ddtg.html>ddt<https://www.few.vu.nl/~trt800/ddtg.html>g.html<https://www.few.vu.nl/~trt800/ddtg.html>

We hope to see many of you next week!

Alvaro, Federica and Thomas

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/20250528/167b9bc4/attachment.html>