Lecture Series: "Collective dynamics of active particles "

Professor Eitan Tadmor is a ​2024/2025 Lowy Distinguished Guest Professor of The Institute of Advanced Studies.

Syllabus

Nature and human societies offer many examples of self-organized behavior: ants form colonies, birds flock, mobile networks synchronize, and consensus may emerge from interaction of diverse human opinions. These are examples of collective dynamics in which small scale interactions of so-called active particles, lead to the emergence of large-scale patterns.
 

We will survey recent mathematical developments in collective dynamics, covering four main topics.

1. Environmental averaging. Agent-based description of swarm dynamics on graphs, governed
by different protocols of alignment, attraction, repulsion, anticipation. Collisions are avoided.

2. Mean-field. From empirical measure to mean-field limit — the passage to kinetic
description.

3. Large crowd dynamics. The passage to hydrodynamic description. Closure of moments,
pressure and energy fluctuations.

4. Large time dynamics. How different protocols of communication affect non-equilibrium
fluctuations, leading to the emergence of consensus, flocking, multi-species, etc.