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<p class="MsoNormal"><span lang="EN-US">Dear all,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Samuel and Lauran are going to speak on <o:p>
</o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:3.75pt;margin-right:0cm;margin-bottom:7.5pt;margin-left:0cm;background:white">
<b><span style="font-size:11.5pt;font-family:Helvetica;color:black;mso-fareast-language:EN-GB">Foliations and equivariant diffeomorphism groups [Chap. 2, Ban]<o:p></o:p></span></b></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">This Friday we have a DDT&G in Leiden.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">As I’m traveling I won’t make it to both events, but I wish you good times!<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Best,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Thomas<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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<span style="font-size:11.5pt;font-family:Helvetica;color:black">31-10-2025: 14:30-17:00 Leiden, Gorlaeus Building, room BW.0.20 <a href="https://webspace.science.uu.nl/~kool0009/">Martijn Kool </a>: Isotropic Hopf index for orthogonal bundles and Magnificent
Four<o:p></o:p></span></h4>
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<span style="font-size:9.0pt;font-family:Helvetica;color:black">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.<br>
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.<br>
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.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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