Since before entering university, I have had a profound interest in mathematics, particularly in topology and geometry. My fascination was sparked by topics such as cosmology based on the theory of relativity, black holes, quantum mechanics, and the essence and characteristics of the shapes we know. Initially, my ambition was to pursue physics to study geometric models of the universe grounded in differential geometry and topology. However, upon receiving advice from various seniors and professors that these topics are actively researched in the field of differential geometry and topology, I decided to pursue a major in mathematics with a dream of delving into differential geometry and topology.
I have actively participated in conferences, particularly those related to geometric analysis. I attended the Einstein & Harmonic Manifold conference organized by Professor Park Jung-hyung of Sungkyunkwan University and Professor Lee Gye-seon of Seoul National University. Additionally, I participated in the Minimal Surface School and Jaigyoung Choeโs 70th-anniversary conference organized by the Korea Institute for Advanced Study. During these conferences, I engaged in in-depth discussions with Professor Kyeongsu Choi of KIAS about geometric analysis. I am currently taking Professor Kyeongsu Choiโs class on geometric PDE. At Jaigyoung Choeโs conference, I had the opportunity to discuss topics related to the Penrose Inequality in General Relativity with Richard Schoen.
I also attended a conference organized by the Korean Mathematical Society, where I had the chance to ask questions about the visualization of minimal surfaces to Professor Yang Sung-deok of Korea University. I received valuable assistance from Professor Yang Sung-deok and engaged in discussions with Professor Joseph Cho of TU Wien about discrete differential geometry.
I once studied optimization and observed similarities between basic ideas in optimization and those used in geometric flow.
In the case of topology, I focused more on practical applications than conference attendance. I took coursework in algebraic topology and low-dimensional topology, studying topics such as the Jones Polynomial for knot classification and Khovanov Homology. Currently, I am working with Professor Seungwon Kim, using Fox Calculus to compute knots on given differentiable manifolds.
I have a slight interest in numerical PDE. After taking a course on the finite difference method, I used it for my final project to solve the Schrรถdinger equation. I presented this project at Ajou University and attempted to implement numerical approximations for the curve shortening flow using FDM, inspired by the project.
COVID-19 has significantly transformed my life as a student. Before COVID-19, I exclusively attended offline classes, but I was forced to adapt to online learning. Initially, it was challenging as I missed the atmosphere and the ability to ask questions freely. This experience became the catalyst for my temporary leave of absence, during which I explored diverse non-academic experiences.
The most significant gain during my hiatus was the development of teaching skills. During my leave, I served as a homeroom teacher for about 70 high school students preparing for Korean university entrance exams. Unable to teach in person due to COVID-19, I adopted a flipped learning approach. I used video media and learned LaTeX to create high-quality materials for distribution. I created an interactive online environment using various platforms, encouraging students to share thoughts and engage in discussions. This unconventional teaching method sparked interest among students, leading to a deeper understanding, and approximately 80% of them achieved excellent scores on their respective school exams.
I also taught a college student subjects such as Calculus 1 & 2, Ordinary Differential Equations, Linear Algebra, and Engineering Mathematics. The student lacked a strong foundation in mathematics, but through supplementary lessons and materials, I bridged the gap. Emphasizing the organic connection between calculus and linear algebra, I elevated their understanding to a level where they could ask questions about ODE and Engineering Math.
Of course, my hiatus was not without challenges. I faced difficulties in devoting time to my own mathematical studies due to responsibilities towards the students I taught. Despite this, I diligently supplemented my knowledge in Abstract Algebra 1 and Numerical Analysis. In Abstract Algebra, I retook the course to better understand the material and created resources for the mathematics and physics society, of which I was the president.
For Numerical Analysis, I conducted additional study sessions, preparing Python skeleton code for practical understanding. These efforts led to an interview request from the school for an exemplary student-led class, which was later featured on the schoolโs website.
I am currently serving as the president of the mathematics academic club, MIMIC, at Sungkyunkwan University. This club focuses on individual presentations on topics of interest in mathematics, as well as tutoring and volunteer activities. I manage the clubโs YouTube channel, โMIMIC SKKU,โ and its website.
I have given four presentations within the club. The topics included a seminar on โNon-Euclidean Parallel Postulateโ for lower-class students, an exploration of the Jones Polynomial in Knot Theory with connections to Quantum Invariants, a session on solving the Schrรถdinger equation using the Finite Difference Method, and a presentation on the Curve Shortening Flow in 2D plane, which is related to geometric PDE.
Upon Professor Youngjoon Hongโs request, I manage the universityโs computer server room for machine learning research. I collaborated with Professor Seungwon Kim on using the server to compute invariants for knots.
I received numerous scholarships during my undergraduate years, including the departmentโs academic excellence scholarship, the universityโs presidentโs scholarship, and scholarships from the Korea Science and Engineering Foundation and the Korea Foundation for Advanced Studies. Also, in 2021, I secured second place and received a silver award at the University Students Contest of Mathematics organized by the Korean Mathematical Society.
Due to my interest in geometry and topology, I pursued advanced courses not typically available to undergraduates. Examples include courses on Sobolev spaces in PDE, low-dimensional topology, knot theory in three dimensions, Riemannian geometry, and geometric PDE covering curve shortening flow and mean curvature flow. Through the Undergraduate Research Program, I delved into topics not covered in undergraduate studies. Despite the absence of courses on smooth manifolds and knot theory, I worked with professors to study โGeometry of Differential Formsโ and โIntroduction to Smooth Manifold,โ creating lecture notes for the latter. I also explored topics in โGauge Fields, Knots, and Gravityโ related to topological quantum field theory.
These experiences have shaped my academic journey, fueling my passion for mathematics and teaching while providing me with a diverse skill set and a deep understanding of mathematical concepts.