Stochasticity can play an important role in the dynamics of biologically relevant populations.
These span a broad range of scales: from intra-cellular populations of molecules to …

This tutorial article introduces the physics of quantum information scrambling in quantum
many-body systems. The goals are to understand how to precisely quantify the spreading of …

Over the past 30 years, one of the most rapidly expanding areas in ecology has been the
development of structured population models, where individuals have attributes such as …

These notes attempt to provide an elementary introduction to the one-dimensional discrete-
time branching random walk and to exploit its spinal structure. They begin with the case of …

The genetic diversity of a species is shaped by its recent evolutionary history and can be
used to infer demographic events or selective sweeps. Most inference methods are based …

Thermalization of chaotic quantum many-body systems under unitary time evolution is
related to the growth in complexity of initially simple Heisenberg operators. Operator growth …

Traveling waves are ubiquitous in nature and control the speed of many important
dynamical processes, including chemical reactions, epidemic outbreaks, and biological …

Epidemics, flame propagation, and cardiac rhythms are classic examples of reaction–
diffusion waves that describe a switch from one alternative state to another. Only two types of …

A novel strategy for controlling the spread of arboviral diseases such as dengue, Zika and
chikungunya is to transform mosquito populations with virus-suppressing Wolbachia. In …

We consider a family of models describing the evolution under selection of a population
whose dynamics can be related to the propagation of noisy traveling waves. For one …