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<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">Dear topologists,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">The next talk in the GeoTop Seminar is by Hannah, who is going to join us as postdoc in January! I will attend the talk live at the department, please join me if you are interested.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">5pm, Friday 1.11, Maryna.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">I also want to catch up on a recorded talk from the knot theory online seminar on Seifert surfaces of alternating knots in 4D:<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">3pm, Monday 4.11, Maryna.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">Abstracts below.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">Best,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">Senja<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><span lang="EN-US" style="mso-fareast-language:EN-US">Hannah Santa Cruz<o:p></o:p></span></b></p>
<p class="MsoNormal"><b><span lang="EN-US" style="mso-fareast-language:EN-US">November 1, 2024</span></b><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><b><span lang="EN-US" style="mso-fareast-language:EN-US">Title: </span></b><span lang="EN-US" style="mso-fareast-language:EN-US">Hodge Laplacians on Sequences<o:p></o:p></span></p>
<p class="MsoNormal"><b><span lang="EN-US" style="mso-fareast-language:EN-US">Abstract: </span></b><span lang="EN-US" style="mso-fareast-language:EN-US">Hodge Laplacians have been previously proposed as a natural tool for understanding higher-order interactions
in networks and directed graphs. In this talk, we will cover a Hodge-theoretic approach to spectral theory and dimensionality reduction for probability distributions on sequences and simplicial complexes. We will introduce a feature space based on the Laplacian
eigenvectors associated to a set of sequences, and will see these eigenvectors capture the underlying geometry of our data. Furthermore, we will show this Hodge theory has desirable properties with respect to natural null-models, where the underlying vertices
are independent. Specifically, we will see the appropriate Hodge Laplacian has an integer spectrum with high multiplicities, and describe its eigenspaces. Finally, we will cover a simple proof showing the underlying cell complex of sequences has trivial reduced
homology.<o:p></o:p></span></p>
<p class="MsoNormal"><b><span lang="EN-US" style="mso-fareast-language:EN-US">Keywords: </span></b><span lang="EN-US" style="mso-fareast-language:EN-US">TDA, Hodge Laplacians, sequential data.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><a href="https://seminargeotop-a.com/next-talks">https://seminargeotop-a.com/next-talks</a><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">Knot online seminar
</span><span style="mso-fareast-language:EN-US"><a href="https://k-os.math.ethz.ch/video-kos.html"><span lang="EN-US">https://k-os.math.ethz.ch/video-kos.html</span></a></span><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p></o:p></span></p>
<ul style="margin-top:0cm" type="disc">
<li class="MsoNormal" style="mso-list:l0 level1 lfo1"><span lang="EN-US" style="mso-fareast-language:EN-US">Speaker: </span><span style="mso-fareast-language:EN-US"><a href="https://web.ma.utexas.edu/users/mhm799/"><b><span lang="EN-US">Maggie Miller</span></b></a></span><span lang="EN-US" style="mso-fareast-language:EN-US"> (University
of Texas at Austin)<o:p></o:p></span></li><li class="MsoNormal" style="mso-list:l0 level1 lfo1"><span lang="EN-US" style="mso-fareast-language:EN-US">Title: <b>Seifert surfaces of alternating knots in 4D</b> (on </span><span style="mso-fareast-language:EN-US"><a href="https://arxiv.org/abs/2406.11718"><span lang="EN-US">2406.11718</span></a></span><span lang="EN-US" style="mso-fareast-language:EN-US">)<o:p></o:p></span></li><li class="MsoNormal" style="mso-list:l0 level1 lfo1"><span lang="EN-US" style="mso-fareast-language:EN-US">Abstract: We show that any two same-genus, oriented, boundary parallel surfaces bounded by a non-split alternating link into the 4-ball are smoothly
isotopic fixing boundary. In other words, a non-split alternating link bounds a unique Seifert surface up to isotopy in the 4-ball (and up to genus).
</span><span style="mso-fareast-language:EN-US">This is joint with Seungwon Kim and Jaehoon Yoo.<o:p></o:p></span></li></ul>
<p class="MsoNormal"><span style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:12.0pt">---------------------------------------------</span><o:p></o:p></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:12.0pt">Dr S. Barthel</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:12.0pt">Assistant professor in mathematics</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Vrije Universiteit Amsterdam</span><o:p></o:p></p>
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