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Hao-Yang Yen

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Research Interests

My research spans statistical physics, celestial mechanics, dynamical systems, and mathematical physics. I investigate the statistical behavior of complex and stochastic dynamical systems—such as epidemic and ecological models—and study physical systems, particularly celestial mechanics and statistical physics, utilizing the mathematical structures of differential geometry and algebraic geometry. I am also interested in the interfaces between statistical physics, data science, and number theory.

  • Stochastic dynamics: spectra, mixing, universality, rare events
  • Celestial mechanics: N-body stability, central configurations, symmetry, ergodicity
  • Bridges: statistical physics/dynamical system × number theory/data science
Central configuration on a circumscribed circle
A central configuration whose center of mass lies at the circumcenter.
Lorenz attractor
Lorenz attractor — a classic minimal chaotic climate model.
Arnold's cat map
Arnold’s cat map: ergodicity, mixing, chaos—at a glance.
Reaction–diffusion pattern formation
Self-organized pattern formation in driven–dissipative media.
Turbulence eclogical model
Ecological A-B-E model for turbulence.

Related Simulation of Research

Current Research Areas

Stochastic Dynamics

Tensor Networks for Classical Stochastic Systems

We investigate why tensor networks—originally for quantum many-body systems—can model classical stochastic dynamics. By clarifying the underlying principles beyond 1D cases, we connect quantum and classical formalisms through operator/spectral viewpoints.

  • Tensor networks
  • Rare events
  • Stochastic processes
  • Many-body
Spectral Theory

Spectra, Phase Transitions & Universality

Stochastic generators expose deep links between spectra and macroscopic behaviors. I study how eigenvalue distributions relate to universality classes in nonequilibrium systems. Currently, I found spectral topology can affect dynamics and phase transitions in turbulence.

  • Generators
  • Turbulence
  • Spectral gap
  • Spectral topology
  • Phase transition and universality
Celestial Mechanics

Central Configurations & Symmetry Breaking

Central configurations yield self-similar N-body motions (homothetic expansion/contraction or rigid rotation). I explore analogies to symmetry breaking in statistical physics and map phase-diagram-like structures for symmetric 5-body configurations.

  • Hamiltonian dynamical systems
  • N-body
  • Symmetry
  • Bifurcation
  • Computer Algebra