Research Experience
I derived a precise estimate for the mean extinction time of the contact process on stars. I incorporated special function theoretic techniques to perform a detailed energy landscape analysis, then applied the potential-theoretic approach to metastability. This novel integration of methodologies, previously unutilized in this context, successfully computed the first sharp estimate. I submitted a research paper, and delivered talks at the Cornell Probability Summer School and the 2024 KMS Annual Meeting.
Arithmetic Dynamics of Polynomial Maps
I initially studied the arithmetic dynamics of rational maps, focusing particularly on Silverman's approach to the equality of the field of definition and the field of moduli. This involved examining the cohomology structure of rational maps and the theory of algebraic curves. Subsequently, I investigated sharp uniform bounds on the periodic orbit size for integral polynomial maps on the affine plane. By developing a local–global principle for periodic orbit types, I demonstrated the existence of large periodic orbits.
- [2024/03/22] Local–global principle for periodic orbit types (notes)
- [2024/09/24] Existence of large periodic orbits (notes)
EVT and Geodesic Coding for Generalized Continued Fractions
I initially studied the ergodic theory of the geodesic flow on modular surfaces and its connection to continued fractions through geodesic coding. Next, I explored Pollicott's extreme value theorem (EVT) for geodesic excursions on the modular surface, derived from Galambos's EVT for continued fractions. Subsequently, I surveyed the EVT for generalized continued fractions to address higher dimensional generalizations of Pollicott's EVT. I independently continued my studies during my mandatory service in the Korean Army.