[Topology.beta] Fwd: DDT&G seminar tomorrow @Leiden: Martijn Kool

[Rot, T.O. (Thomas)]

Begin forwarded message:

From: "Pasquotto, F. (Federica)" <f.pasquotto at math.leidenuniv.nl>
Date: 30 October 2025 at 10:30:35 CET
To: "Pasquotto, F. (Federica)" <f.pasquotto at math.leidenuniv.nl>
Subject: DDT&G seminar tomorrow @Leiden: Martijn Kool


Dear all,

This is a gentle reminder of tomorrow's Dutch Differential Topology and Geometry seminar, which will take place in Leiden.

Speaker: Martijn Kool<https://www.uu.nl/medewerkers/MKool1> (Utrecht)
Title: Isotropic Hopf index for orthogonal bundles and Magnificent Four
Date: Friday 31 October, 14:30-17:00
Location: Leiden, Gorlaeus Building, room BW.0.20

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 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 tomorrow in Leiden!

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.






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