Mathematical Colloquium

abstract: Mathematics has always been inspired by thinking about the natural world and aiming to understand phenomena surrounding us. The talk is aimed to be an invitation to follow on a naturally personal route, exploring applications of mathematical research in the eld of natural sciences. As for the rst part, we will depart from a naively posed question in image processing and consider it as leading to work on a particular class of kernels for data-driven analysis on spheres. Moving beyond the original problem, insights into classes of zonal kernels for the sphere also provide a better understanding of widely used models of similarity in the Euclidean space.

To move the other way round, we will consider a completely dierent eld of application, asking what mathematical tools can be applied to gain a better understanding of complex adaptive systems. Taking in the abstract perspective of mathematics, allows for a generic view onto such systems, leading to an approach for inference, which is independent of the concrete instantiation of the system. Doing so, we can discuss more general questions on what constitutes the essence of evolution and how to identify its traces in natural phenomena.

Summarizing, both examples stand for the strong belief in interdisciplinary scientic work as a joint adventure at eye level, rather than the softening blur of a little bit of everything.

This is a hybrid talk, live in lecture hall A027 and synchronous broadcast via the following zoom-link:

Join Zoom Meeting: https://lmu-munich.zoom.us/j/99946902916?pwd=UWM5SGtIL091NmdjU3BHVVpOU0lEdz09

Meeting ID: 999 4690 2916, Passcode: 695211