University of Amsterdam

My talk will have two parts. First, I will tell you how a single cell produces light to survive; then, I will explain how a huddle of chloroplasts in cells form glasses to optimize plant life. Part I: Bioluminescence (light generation in living organisms) has mesmerized humans since thousands of years ago. I will first go over the recent progress in experimental and mathematical biophysics of single-cell bioluminescence (PRL 125 (2), 028102, 2020) and then will go beyond and present a lab-scale experiment and a continuum model of bioluminescent breaking waves. Part II: To remain efficient during photosynthesis, plants can re-arrange the internal structure of cells by the active motion of chloroplasts. I will show that the chloroplasts can behave like a densely packed light-sensitive active matter, whose non-gaussian athermal fluctuations can lead to various self-organization scenarios, including glassy dynamics under dim lights (PNAS 120 (3), 2216497120, 2023). To this end, I will also present a simple model that captures the dynamic of these biological glasses.

The SI model is the most basic of all compartmental models used to describe the spreading of information through a population. In this talk we will present a mathematical formalism to solve the SI model on generic networks. Our methods rely on a tensor product formulation of the dynamical spreading process, inspired by many-body quantum systems. Here we will focus on time-dependent expectation values for the state of individual nodes, which can be obtained from contributions of subgraphs of the network. We show how to compute these contributions systematically and derive a set of symmetry relations among subgraphs of differing topologies. We conclude by comparing our results for small sample networks to Monte-Carlo simulations and mean-field approximations.

arXiv link: https://arxiv.org/abs/2109.03530

We give a description of the category of ordinary K3 surfaces over a finite field in terms of linear algebra data over Z. This gives an analogue for K3 surfaces of Deligne's description of the category of ordinary abelian varieties over a finite field, and refines earlier work by N.O. Nygaard and J.-D. Yu. Two important ingredients in the proof are integral p-adic Hodge theory, and a description of CM points on Shimura stacks in terms of associated Galois representations. References: arXiv:1711.09225, arXiv:1707.01236.