Topic of Research Seminar: Moving Through and Across Disciplines: A Rewarding Journey in Studying Biology Through the Lens of Mathematics

Abstract: Quantifying how spatial disorder affects the movement of a diffusing particle or an agent is fundamental to a myriad of applications across disciplines. When diffusion occurs on a network, that is on a highly disordered environment, predicting the movement dynamics of an agent has relied so far on estimates provided by stochastic simulations, rather than rigorous mathematical tools. To close this knowledge gap I have devised a general methodology to represent analytically the movement and search dynamics of a diffusing random walk on sparse graphs. I show its utility by uncovering the existence of a bi-modality regime in the time-dependence of the first-passage probability to hit a target node in a small-world network. By identifying the network features that give rise to the bi-modal regime, I challenge long-held beliefs on how the statistics of the so-called direct, intermediate, and indirect trajectories influence the shape of the resulting first-passage and first-absorption probabilities and the interpretation of their mean values.

Name of Speaker: Prof. Luca Giuggioli

Professorial Rank of Speaker: Professor of Complexity Sciences

Affiliation of Speaker: University of Bristol, UK

Date and Venue: (Wednesday) 17 September, 2025, 03:30 PM, Seminar Hall, School of Mechanical and Manufacturing Engineering (SMME), NUST Islamabad