Vorträge in der Woche 14.07.2025 bis 20.07.2025

Mittwoch, 16.07.2025: What is (Mathematically) a Neural Network?

Dr. Armando Cabrera Pacheco (Universität Tübingen)

Given the hype surrounding machine learning and artificial intelligence, it is natural to be curious about what neural networks are and how they work. However, while there is a lot of information on the subject, it is not easy to find it in a form suitable for (some) mathematicians. When looking for a concrete explanation of what neural networks are, one often finds analogies related to neuroscience and not much of the actual mathematical framework behind them, which often leaves mathematicians unsatisfied. In this talk, we will look at neural networks from a purely mathematical point of view. We will discuss some of the straightforward challenges, both from a mathematical and computational viewpoint, that these powerful tools present.

Donnerstag, 17.07.2025: Cosmological quantum fields, Minkowski-like vacua and Dark Energy

Nicolai Rothe (TU Berlin)

We will discuss some newly found solutions to the full massless semiclassical Einstein equation (SCE) in a cosmological setting (with lambda=0). After a short introduction to the relevant notions, we present the SCE in a particular shape which allows for the construction of certain vacuum states. These states may be viewed as the least possible generalization of the Minkowski vacuum to generic cosmological space-times. In this setting, solving the SCE breaks down into solving a certain ODE which can be approached numerically and, at least generically, we obtain solutions that well fit physical expectations. Moreover, these solutions indicate dark energy as a quantum effect back-reacting on cosmological metrics and, since in our model m=lambda=0, this may not be traced back to the usual, obvious dark-energy/cosmological constant effect of a quantum field.

Freitag, 18.07.2025: Strenge Kommutativität von höheren Homotopiegruppen

Philipp Schmale (Uni Tübingen)