The Quantum Chaos of Real-World Networks

Abstract: Modern science increasingly relies on predictions derived from massive, interconnected data sets—from social networks to neural activity to the internet. To understand these complex systems, we must move beyond surface-level correlations and uncover the fundamental principles that govern their structure and dynamics. Surprisingly, a fruitful way to analyze these networks is to use the framework created to study atoms in quantum systems. In this talk, I will discuss recent progress in analyzing large networks through the lens of spectral graph theory and quantum chaos. This perspective reveals deep connections between randomness, geometry, and statistical physics, allowing us to prove sharp results about the universal behavior of large networks. I’ll trace the development of these ideas from classical spectral graph theory to modern advances inspired by quantum chaotic systems, and highlight how these methods provide new tools for distinguishing order from noise in complex data. I’ll conclude by discussing open questions and emerging directions at the intersection of network science, probability, and mathematical physics.

Speaker bio: Theo McKenzie is a postdoctoral fellow at Stanford University studying probability theory through the lens of random graphs. Specifically, he studies the relationship between the spectral geometry of graphs and quantum chaos. Previously, he was a PhD student at Berkeley and a postdoctoral fellow at Harvard.

Moderator: This talk is moderated by Ted Theodosopoulus. Ted is a mathematician who, after working for years in academia and industry, transitioned to teaching at the pre-college level sixteen years ago, the last eight at Nueva, where he teaches math and economics. Ted’s research background is in the area of interacting stochastic systems, with particular applications in biology and economics.

Computer scienceMathematics

Audience: researchers in the topic

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Relatorium seminar

Series comments: The name "Relatorium" combines "relator" with the Latin root "-ium," meaning "a place for activities" (as in "auditorium" or "gymnasium"). This seminar series is a platform to relate ideas, interact with math, and connect with each other.

In this series, we explore math beyond what we usually hear in standard talks. These sessions fall somewhere between a technical talk and a podcast: moderately formal, yet conversational. The philosophy behind the series is that math is best learned by active participation rather than passive listening. Our aim is to “engage and involve,” inviting everyone to think actively with the speaker. The concepts are accessible, exploratory, and intended to spark questions and discussions.

The idea of relatability has strong ties to compassion — creating space for shared understanding and exploration - which is the spirit of this seminar! This is a pilot project, so we’re here to improvise, learn, and evolve as we go!

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