Active matter describes systems whose constituents generate non-conservative forces on their environment, leading to the wealth of emergent phenomena encountered in the living world. To study their self-organization, the first step is to identify the relevant slow modes describing the collective structures that emerge, from scalar fields to polar and nematic modes.

In this talk, I will discuss two examples of self-organization in active systems: one scalar system, and one where polar and nematic order interact.
In the first part, I will investigate the role of random motility regulation in the self-organization of microbial ecosystems consisting of N >>1 species. Relying on particle-based simulations, coarse-graining methods and random matrix theory, I will show how weak random interactions are sufficient to fragment the ecosystem into distinct, spatially segregated communities.

In the second part, I will consider system where polar and nematic order couple to one another, a situation encountered both in epithelial tissues and in cytoskeletal filaments. This coupling produces string-like topological defects or topological strings. In a compressible fluid where the density field undergoes continuous turnover, topological strings are stabilized into non-equilibrium configurations, revealing the subtle interplay between scalar, polar and nematic order in active matter.