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Begin forwarded message:<br>
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<div dir="ltr"><b>From:</b> "Pasquotto, F. (Federica)" <f.pasquotto@math.leidenuniv.nl><br>
<b>Date:</b> 30 October 2025 at 10:30:35 CET<br>
<b>To:</b> "Pasquotto, F. (Federica)" <f.pasquotto@math.leidenuniv.nl><br>
<b>Subject:</b> <b>DDT&G seminar tomorrow @Leiden: Martijn Kool</b><br>
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Dear all, </div>
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This is a gentle reminder of tomorrow's Dutch Differential Topology and Geometry seminar, which will take place in Leiden. </div>
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<b><br>
Speaker</b>:<a style="margin: 0px;" data-auth="NotApplicable" data-linkindex="0" rel="noopener noreferrer" title="https://www.uu.nl/medewerkers/MKool1" class="x_OWAAutoLink" id="OWA5e7ae447-fc99-f769-bbe2-7f7bb4cfd1d5" target="_blank" href="https://www.uu.nl/medewerkers/MKool1"> Martijn
Kool</a> (Utrecht)</div>
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<b>Title</b>: <i>Isotropic Hopf index for orthogonal bundles and Magnificent Four</i></div>
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<b>Date</b>: Friday 31 October, 14:30-17:00</div>
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<b>Location</b>: Leiden, Gorlaeus Building, room BW.0.20</div>
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The schedule will be as follows:</div>
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2:30-3:30 p.m.: first part of the seminar (little to no prior knowledge assumed)</div>
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4:00-5:00 p.m.: second part of the seminar (slightly more advanced level)</div>
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Please visit the seminar's webpage for additional information and an overview of past and upcoming talks:</div>
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<span style="color: blue;"><u><a style="color: blue; margin: 0px;" data-loopstyle="linkonly" data-safelink="true" data-linkindex="1" data-auth="NotApplicable" originalsrc="https://www.few.vu.nl/~trt800/ddtg.html" rel="noopener noreferrer" title="Original URL: https://www.few.vu.nl/~trt800/ddtg.html. Click or tap if you trust this link." class="x_x_x_x_x_x_x_x_x_x_x_ContentPasted1 x_x_x_x_x_x_x_x_x_x_OWAAutoLink x_x_x_x_x_x_x_x_x_x_ContentPasted0 x_x_x_x_x_x_x_x_x_ContentPasted0" id="OWA14315008-cda3-c814-b29f-0e436969e529" target="_blank" href="https://www.few.vu.nl/~trt800/ddtg.html">https://www.few.vu.nl/~trt800/</a></u></span><span style="color: rgb(7, 7, 6);"><u><a style="color: rgb(7, 7, 6); margin: 0px;" data-loopstyle="linkonly" data-safelink="true" data-linkindex="2" data-auth="NotApplicable" originalsrc="https://www.few.vu.nl/~trt800/ddtg.html" rel="noopener noreferrer" title="Original URL: https://www.few.vu.nl/~trt800/ddtg.html. Click or tap if you trust this link." class="x_x_x_x_x_x_x_x_x_x_x_ContentPasted1 x_x_x_x_x_x_x_x_x_x_OWAAutoLink x_x_x_x_x_x_x_x_x_x_ContentPasted0 x_x_x_x_x_x_x_x_x_ContentPasted0" id="OWA0091f5b4-5c2a-a0ce-e5a2-0230b9acdf1d" target="_blank" href="https://www.few.vu.nl/~trt800/ddtg.html">ddt</a></u></span><span style="color: blue;"><u><a style="color: blue; margin: 0px;" data-loopstyle="linkonly" data-safelink="true" data-linkindex="3" data-auth="NotApplicable" originalsrc="https://www.few.vu.nl/~trt800/ddtg.html" rel="noopener noreferrer" title="Original URL: https://www.few.vu.nl/~trt800/ddtg.html. Click or tap if you trust this link." class="x_x_x_x_x_x_x_x_x_x_x_ContentPasted1 x_x_x_x_x_x_x_x_x_x_OWAAutoLink x_x_x_x_x_x_x_x_x_x_ContentPasted0 x_x_x_x_x_x_x_x_x_ContentPasted0" id="OWA96b2d6ce-9b66-75fd-6a12-d20377448ff2" target="_blank" href="https://www.few.vu.nl/~trt800/ddtg.html">g.html</a></u></span></div>
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We hope to see many of you tomorrow in Leiden!</div>
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Alvaro, Federica and Thomas</div>
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<b>Abstract</b></div>
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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.</div>
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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.</div>
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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.</div>
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Classified as Internal | Intern</div>
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