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<p class="MsoNormal"><span style="color:black">Dear all, <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">You are cordially invited to attend the next Dutch Differential Topology and Geometry seminar, which will take place next week in Leiden. <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Speaker</span></b><span style="color:black">: <a href="https://www.uu.nl/medewerkers/MKool1" title="https://www.uu.nl/medewerkers/MKool1">Martijn Kool</a> (Utrecht)<o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Title</span></b><span style="color:black">:
<i>Isotropic Hopf index for orthogonal bundles and Magnificent Four</i><o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Date</span></b><span style="color:black">: Friday 6 June, 14:30-17:00<o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Location</span></b><span style="color:black">: Leiden, Gorlaeus Building, room BW.0.19<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">The schedule will be as follows:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black">2:30-3:30 p.m.: first part of the seminar (little to no prior knowledge assumed)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black">4:00-5:00 p.m.: second part of the seminar (slightly more advanced level)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">Please visit the seminar's webpage for additional information and an overview of past and upcoming talks:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><br>
</span><u><span style="color:blue"><a href="https://www.few.vu.nl/~trt800/ddtg.html" target="_blank" title="Original URL: https://www.few.vu.nl/~trt800/ddtg.html. Click or tap if you trust this link.">https://www.few.vu.nl/~trt800/</a></span></u><u><span style="color:#070706"><a href="https://www.few.vu.nl/~trt800/ddtg.html" target="_blank" title="Original URL: https://www.few.vu.nl/~trt800/ddtg.html. Click or tap if you trust this link."><span style="color:#070706">ddt</span></a></span></u><u><span style="color:blue"><a href="https://www.few.vu.nl/~trt800/ddtg.html" target="_blank" title="Original URL: https://www.few.vu.nl/~trt800/ddtg.html. Click or tap if you trust this link.">g.html</a></span></u><o:p></o:p></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">We hope to see many of you next week!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">Alvaro, Federica and Thomas<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:black">Abstract</span></b><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:black">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.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black">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.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black">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>
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