Johannes Zimmer (TUM): Wednesday, 10. July 16:00 - 17:00 

Many processes in nature can be modeled on different scales; for

example with 'high resolution' using particles or 'zoomed out' using

partial differential equations (PDEs). One interest covered in this talk is

the derivation of PDEs describing the collective behaviour of (infinitely)

many particles: Can we derive the PDE? Can we machine learn the PDE from

particle data? It turns out that it is often important to understand the

structure of the equations; on the level of PDEs, a thermodynamic structure

based on energy and entropy is very helpful and will be described. The arrow

of time will play a central role: Small-scale models (of particle type) are

often can be reversible in time, while the large-scale description (of PDE type)

is irreversible. This seems at first puzzling, as the two models describe the

same system. We will discuss some mathematical approaches to understand this.

Craig Kaplan (University of Waterloo), TUM HS3: Mittwoch, 12. Juni, 14:30 - 15:30

Polyforms—shapes constructed by gluing together copies of cells in an underlying grid—are a convenient experimental tool with which to probe problems in tiling theory.  Unlike shapes more generally, they can be enumerated exhaustively, and are amenable to analysis using discrete computation.  Furthermore, polyforms appear to be quite expressive in terms of the range of tiling-theoretic behaviours they can exhibit.  I discuss the computation of isohedral numbers and Heesch numbers, both of which are connected to a variety of unsolved problems in tiling theory, and the connection of these problems to the world's first aperiodic monotiles, discovered in 2023.

Coffee afterwards