In September 2023, I gave an introductory talk at K-Garage G++ Math Seminar, a peer seminar on diverse topics in mathematics. I introduced important concepts that appear in probability theory: phase transition, mixing time, cutoff, and metastability.
This post is based on my talk in August 2023 at the Graduate Probability Reading Seminar in percolation and random-cluster model, supervised by Prof. I. Seo. I, jointly with Jeonghyun Ahn, covered the materials from chapter 6 of Grimmett’s textbook [6]—about the planar duality, critical probability, and the first order phase transition of the random-cluster model on the planar square lattice—with some additional remarks on recent progresses made by Duminil-Copin and his coresearchers.
This post is based on my talk in June 2023 at the Graduate Probability Reading Seminar in percolation and random-cluster model, supervised by Prof. I. Seo. I covered the materials from chapter 4 of Grimmett’s textbook [3]—about the free energy $\kappa$ of percolation on hypercubic lattices and its differentiability properties—with some additional remarks on historical background and recent progresses.
During this winter vacation, I conducted a 9-lecture course previewing the upcoming semester’s major subject Introduction to Mathematical Analysis (with practice) 1 in the College of Natural Sciences, Seoul National University. Below are lecture notes that briefly summarize the past classes.
This post is a wrap-up of the research internship, advised by Prof. S. Lim. We review previous studies that are related to the extreme value problem on generalized continued fractions.