The geometry of influence inside clustered systems
Adler’s Algorithm is the informal name for my PhD research in mathematics at Princeton University. At its core, it studies how tightly connected networks behave under pressure — how clusters form, interact, and influence each other inside complex systems.
The work lives at the intersection of graph theory, dynamics, and game-theoretic intuition. Rather than treating stability as a static property, Adler’s Algorithm asks how patterns of connection and stress propagate through a system over time, and what that reveals about its underlying structure.
John Nash’s work emphasized that equilibrium isn’t just a solution — it reflects how incentives, information, and structure shape one another. Adler’s Algorithm extends that intuition into dense, interconnected networks, asking how cluster geometry influences the behavior of the system as a whole. In this view, stability emerges not from isolated decisions, but from the geometry of the relationships that bind agents together.
Adler’s Algorithm studies what happens inside a network when it is nudged, stressed, or perturbed. It focuses on how clusters form, stabilize, and transmit influence, and how local constraints shape global behavior. The work examines patterns that aren’t visible from individual nodes alone — the way pressure redistributes across boundaries, how tightly knit communities absorb or amplify shocks, and how the geometry of a cluster predicts its long-term dynamics.
While the work is mathematical and abstract, it reflects a broader obsession: understanding how systems behave when they are pushed, distorted, or forced to reveal their deeper shape.
Adler’s Algorithm isn’t a product feature — but it shapes how I design reasoning systems. The work reinforces an instinct that runs through everything I build: that behavior emerges from structure, that explanations should be traceable, and that systems reveal their nature when they’re under pressure. These same principles guide My AI Analyst and the Grok Personas framework, where understanding flows, constraints, and interactions is essential to making intelligence interpretable.