R_1_14 — Biofilms: Microbial Communities, Quorum Sensing, and Cooperation

Biofilms are structured communities of microorganisms — bacteria, archaea, fungi, and algae — attached to surfaces and embedded in a self-produced matrix of extracellular polymeric substances (EPS): polysaccharides, prot

S_5_08 — Digital Privacy: Encryption, Zero-Knowledge Proofs, and Data Sovereignty

Digital privacy — the right of individuals to control their personal information in digital systems — has become one of the defining challenges of the 21st century, driven by the massive expansion of data collection (sur

V_2_21 — Topology Applications in Science

Topology — the branch of mathematics concerned with properties preserved under continuous deformation (stretching, bending, twisting, but not tearing or gluing) — has transformed from an abstract mathematical discipline

V_2_11 — Abstract Algebra: Groups, Rings, and Fields

Abstract algebra is the study of algebraic structures — sets equipped with operations satisfying specific axioms — that generalize familiar arithmetic operations to reveal deep structural patterns across mathematics and

V_2_14 — Differential Topology and Manifolds

Differential topology studies smooth manifolds — spaces that locally resemble Euclidean $\mathbb{R}^n$ with smooth (infinitely differentiable) transition maps — and the smooth maps between them, classified up to diffeomo

V_2_12 — Algebraic Geometry

Algebraic geometry — the study of geometric objects defined by polynomial equations — is one of the most central and technically demanding branches of modern mathematics, connecting algebra, geometry, topology, and numbe

V_2_00 — Pure Mathematics: Subfolder Summary