## Branching random walks: some recent results and open questions

### Nina Gantert

We give an introduction to branching random walks and their continuous counterpart, branching Brownian motion. We explain some recent results on the maximum of a branching random walk and its relation to point processes, as well as a connection with fragmentations. The focus will be on open questions.

**Preparatory reading:**
Lyons and Peres,
Probability on Trees and Networks, Chapters 5.1 (Galton-Watson branching processes) and 13.8 (Tree-indexed random walks)

**Further reading:**

- Zhan Shi, Branching Random Walks
- Julien Berestycki, Topics on Branching Brownian motion
- Ofer Zeitouni, Branching Random Walks and Gaussian Fields

### Accompanying talks:

#### Piotr Dyszewski: Branching random walks and stretched exponential tails

We will consider a branching process with a spacial component on the real line. After birth each individual performs an independent step according a stretched exponential (or Weibull) law. We will give a detailed description of the asymptotic behaviour of the position of the rightmost particle. The talk is based on a ongoing project with Nina Gantert and Thomas Höfelsauer.

#### Sam Johnston: The extremal particles of branching Brownian motion

We study the positions of extremal particles in branching Brownian motion, with a particular emphasis on understanding why moment calculations can be misleading. We then turn to looking at the past trajectories of these particles, as well as their genealogical relationship with other particles in the system.