Mathematics Münster

If we complete the rational numbers $\mathbb{Q}$ with respect to the standard absolute value, we obtain the reals $\mathbb{R}$, wich is a connected topological space. The completion $\mathbb{Q}_p$ of $\mathbb{Q}$ with respect to the $p$-adic valuation for a prime $p$, however, is totally disconnected. So it seems that the concept of a path connecting two points in the $p$-adic numbers $\mathbb{Q}_p$ (or $\mathbb{Q}_p^n$) does not make sense. In fact, the space $\mathbb{Q}_p$ itself is not quite suitable for doing geometry. Instead one can consider the affine line $\mathbb{A}_{\mathbb{Q}_p}^1$ as an adic space. It contains $\mathbb{Q}_p$ as so called \emph{classical points} but has many more points. In this talk we will convince ourselves that $\mathbb{A}_{\mathbb{Q}_p}^1$ is indeed path connected if we use the right notion of a path.

Ever felt unsure what to say, when people ask you what you are working on? Practice your -Science Pitch- to talk about your work at the next conference, collaborator meeting or a family gathering. MM Spotlight on Science Pitch: Friday 25th April 11:00- 12:30 at the SRZ lounge. You will prepare your own pitch and practice in small groups. It's going to be fun and useful! Please let Imke Franzmeier know if you like to participate.

Let X be a proper, smooth rigid space and G a commutative rigid group. We study the relationship between G-representations of the fundamental group of X and G-Higgs bundles on X. This is joint work with Ben Heuer and Mingjia Zhang.

The mathematical core of deep learning is function approximation by neural networks trained on data using stochastic gradient descent.

I will present a collection of results on training dynamics for the deep linear network (DLN). The DLN is a phenomenological model of deep learning for linear functions that was introduced by computer scientists. It allows a comprehensive analysis that reveals interesting ties with several areas of mathematics and several lessons for 'true' deep learning.

This is joint work with several co-authors: Nadav Cohen (Tel Aviv), Kathryn Lindsey (Boston College), Alan Chen, Zsolt Veraszto and Tianmin Yu (Brown).

Origami is not only an art form but also a subject of mathematical interest, especially due to its geometric design. While traditional origami uses straight folds to create flat surfaces, paper can also be bent into curved, developable surfaces. Curved folding enables new modeling possibilities, though it has been less studied. This talk will introduce the speaker's work on curved folding, including artistic examples and design methods. It will also touch on origami's cultural and engineering aspects, and conclude with a hands-on curved folding workshop.

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