Welcome to the Applied Mathematics research group led by Prof. Joon Kyung Lee. Our research focuses on developing and applying mathematical models and computational methods to solve problems in various scientific and engineering disciplines. We are particularly interested in numerical analysis, partial differential equations, scientific computing, and their applications in areas such as fluid dynamics, image processing, and data science. Our goal is to contribute to both theoretical advancements in applied mathematics and practical solutions for real-world challenges.

준경 이 교수님의 응용수학 연구 그룹에 오신 것을 환영합니다. 저희 연구는 다양한 과학 및 공학 분야의 문제 해결을 위해 수학적 모델과 계산 방법을 개발하고 적용하는 데 중점을 둡니다. 특히 수치 해석, 편미분 방정식, 과학 계산, 그리고 유체 역학, 영상 처리, 데이터 과학과 같은 분야에서의 응용에 관심을 가지고 있습니다. 저희의 목표는 응용수학의 이론적 발전과 실제 문제에 대한 실용적인 해결책 모두에 기여하는 것입니다.

Sidorenko's conjecture for blow-ups

More on the Extremal Number of Subdivisions

On tripartite common graphs

Majority dynamics on sparse random graphs

Rainbow Cycles in Properly Edge-Colored Graphs

Sidorenko's conjecture for higher tree decompositions

On the Extremal Number of Subdivisions

Common graphs with arbitrary connectivity and chromatic number

On graph norms for complex‐valued functions

Extended commonality of paths and cycles via Schur convexity

Rainbow cycles in properly edge-colored graphs

Two approaches to Sidorenko’s conjecture

Finite reflection groups and graph norms

On some graph densities in locally dense graphs

Two Remarks on Graph Norms

Counting tree-like graphs in locally dense graphs

Towards Autonomous Mathematics Research

Lower bounds for multivariate independence polynomials and their generalisations

Counting homomorphisms in antiferromagnetic graphs via Lorentzian polynomials

On norming systems of linear equations

Around the positive graph conjecture

On the extremal number of incidence graphs

Chi-boundedness of graphs containing no cycles with k chords

Counting odd cycles in sparse pseudorandom graphs

Domination inequalities and dominating graphs

A proof of the Elliott – Rödl conjecture on hypertrees in Steiner triple systems

Extremal numbers and Sidorenko's conjecture

Finding Increasingly Large Extremal Graphs with AlphaZero and Tabu Search

A Novel Approach to Solving Non-linear PDEs

Efficient Algorithms for Image Denoising using Variational Methods

On graph norms for complex-valued functions

Two remarks on graph norms

Mathematical Modeling of Fluid Flow in Porous Media

More on the extremal number of subdivisions

Convex graphon parameters and graph norms

On the extremal number of subdivisions

Ramsey games near the critical threshold

Some advances on Sidorenko’s conjecture

Rank-width of random graphs

Some advances on Sidorenko's conjecture

Rank‐width of random graphs

Towards autonomous mathematics research

Finding increasingly large extremal graphs with alphazero and tabu search

Extremal numbers and Sidorenko’s conjecture

We prove that every properly edge-colored n-vertex graph with average degree at least 32 (log⁡5n)2 contains a rainbow cycle, improving upon the (log⁡n)2+o(1) bound due to Tomon. We also prove that every properly edge-colored n-vertex graph with at least 105k3n1+1/k edges contains a rainbow 2k-cycle, which improves the previous bound 2ck2n1+1/k obtained by Janzer. Our method using homomorphism inequalities and a lopsided regularization lemma also provides a simple way to prove the Erdős–Simonovits supersaturation theorem for even cycles, which may be of independent interest.

For a graph H, its homomorphism density in graphs naturally extends to the space of two-variable symmetric functions W in Lp, p ≥ e(H), denoted by t(H, W). One may then define corresponding functionals ‖W‖H := |t(H, W)|1/e(H) and ‖W‖r(H) := t(H, |W|)1/e(H), and say that H is (semi-)norming if ‖⋅‖H is a (semi-)norm and that H is weakly norming if ‖⋅‖r(H) is a norm. We obtain two results that contribute to the theory of (weakly) norming graphs. Firstly, answering a question of Hatami, who estimated the modulus of convexity and smoothness of ‖⋅‖H, we prove that ‖⋅‖r(H) is neither uniformly convex nor uniformly smooth, provided that H is weakly norming. Secondly, we prove that every graph H without isolated vertices is (weakly) norming if and only if each component is an isomorphic copy of a (weakly) norming graph. This strong factorisation result allows us to assume connectivity of H when studying graph norms. In particular, we correct a negligence in the original statement of the aforementioned theorem by Hatami.

Sidorenko’s conjecture for blow-ups

Two Approaches to Sidorenko's Conjecture

Joonkyung Lee

Associate Professor

Applied Mathematics

교수님 소개

이준경

연구실 소개

연구실 키워드

알럼나이가 간 회사

연구실 지원 방법

대우 조건

연도별 논문 인용수

저널 & 학회 논문 출판 수

연구실 논문 목록

Towards autonomous mathematics research

Chi-boundedness of graphs containing no cycles with k chords

Counting odd cycles in sparse pseudorandom graphs

연구실 보유 특허

대학별 입시끈

우리 연구실 모집

교수님 소개

이준경

연구실 키워드

알럼나이가 간 회사

연구실 지원 방법

대우 조건

연도별 논문 인용수

저널 & 학회 논문 출판 수

연구실 논문 목록

Towards autonomous mathematics research

Chi-boundedness of graphs containing no cycles with k chords

Counting odd cycles in sparse pseudorandom graphs

연구실 보유 특허

최근 3년간 연구실적 높은 연구실

대학별 입시끈

우리 연구실 모집