**Abstract: -**

Branching random walk is a system of growing particles that starts with one particle. This particle splits into a number of particles, and each new particle makes a displacement independently of each other. The same dynamics goes on and on, and gives rise to a branching random walk, which arises in physics, biology, ecology, etc. It is important because it has connections to various other models in the fields of science mentioned above. In this overview talk, we shall mainly try to address the following question:* if we run a branching random walk for a very very long time and take a snapshot of the particles, what would the entire system look like?* In particular, we shall lucidly discuss how our theorem has verified two conjectures in an important special case. These conjectures were formulated in 2011 by two world-renowned physicists Éric Brunet and Bernard Derrida.

This talk is based on a joint work with ** Ayan Bhattacharya** (now at

**) and**

*Indian Institute of Technology, Bombay***(now at**

*Rajat Subhra Hazra***).**

*Leiden University, The Netherlands***About the Speaker: -**

Parthanil Roy, a mathematician at the Indian Statistical Institute, works on probability theory (stable random fields, extreme values, branching random walks, etc.) with connections to ergodic theory, operator algebra, geometric group theory and hyperbolic dynamics. After completing his PhD from Cornell University and a postdoctoral fellowship at ETH Zurich, Parthanil was a tenure-track assistant professor at Michigan State University before joining Indian Statistical Institute. He has served as the Youth Representative (2017-20) of Bernoulli Society for Mathematical Statistics and Probability, and is currently an editor of Sankhya Series A. He is a recipient of Swarna Jayanti Fellowship (2019-2024) and Young Statistical Scientist Award (2021) from International Indian Statistical Association.