Málstofa: Marton Posfai

Næsta málstofa verður þriðjudaginn 18. apríl kl 13:20 í VHV-023 (ath. ný staðsetning).
Fyrirlesari er Marton Posfai, Central European University, Vienna.
Titill fyrirlestrarins er Physical networks.

Ágrip: Physical networks — networks with nodes and links that are physical objects embedded in space — are shaped by constraints such as volume exclusion, the cost of building and maintaining nodes and links, and local assembly. Although particular physical networks such as neural networks, vascular networks, or electric circuits, have long been studied, the general theoretical framework of physical networks is still in its nascence. In my talk, I will review recent advances in understanding how volume exclusion affects physical networks. First, I will introduce two classes of mathematically tractable network models, each capturing an important aspect of physicality and allowing us to understand mechanisms through which the abstract structure of networks is affected by physical constraints. Then, turning our attention to dynamics on physical networks, I characterize the network’s Laplacian spectrum and show that the Laplacian of the combinatorial network is not sufficient to describe the dynamics on physical networks and that the physical layout must be taken into account by normalizing the Laplacian with the node volume. I will end my talk with a list of open questions.