[Topology.beta] Watch parties online seminar

[Barthel, S.D. (Senja)]

Dear topologists,

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.

5pm, Friday 1.11, Maryna.

I also want to catch up on a recorded talk from the knot theory online seminar on Seifert surfaces of alternating knots in 4D:
3pm, Monday 4.11, Maryna.

Abstracts below.

Best,
Senja

Hannah Santa Cruz
November 1, 2024
Title: Hodge Laplacians on Sequences
Abstract: 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.
Keywords: TDA, Hodge Laplacians, sequential data.
https://seminargeotop-a.com/next-talks


Knot online seminar https://k-os.math.ethz.ch/video-kos.html

  *   Speaker: Maggie Miller<https://web.ma.utexas.edu/users/mhm799/> (University of Texas at Austin)
  *   Title: Seifert surfaces of alternating knots in 4D (on 2406.11718<https://arxiv.org/abs/2406.11718>)
  *   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). This is joint with Seungwon Kim and Jaehoon Yoo.

---------------------------------------------
Dr S. Barthel
Assistant professor in mathematics
Vrije Universiteit Amsterdam
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