The Math & CS Seminar at DePaul


All talks are both in-person and over Zoom, at 2pm, on Fridays.

  • Friday Week 5, Oct 6: Salman Parsa, SoC in Lincoln Park Campus
    Title: Reeb Spaces and the Borsuk–Ulam Theorem
    Abstract: I will talk about Reeb spaces and their discretization called mapper. These are applied tools in topological data analysis. After showing a few examples, I will use the Reeb space to prove a partial extension of the well-known Borsuk-Ulam theorem for maps from \(2\)-sphere into \(\mathbb{R}\). This extension says that there are always two antipodal points \(S^2 \ni x, -x\) such that \(f(x) = f(-x)\) and the two points are connected in the preimage. The proof uses the concept of the Reeb graph which is a 1-dimensional Reeb space. I also consider the relationship between excess homology of the Reeb space of \(f: S^n \to \mathbb{R}^{n - 1}\) and the existence of the analogous extensions of the Borsuk–Ulam theorem for maps into \(\mathbb{R}^m, n > 2\).

  • Friday Week 9, Nov 3: Stefan Mitsch, SoC in Lincoln Park Campus

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