Research

Research Groups

onlinear Complex Systems Lab Infomation
Nonlinear Complex Systems LabWebsite
Research Field Lab Members Mathematical Tools
Analysis of Nonlinear and Collective Dynamics

  1. Stochastic modeling of biochemical systems
  2. Flocking and self-organizing collective dynamics
  3. Mathematical modeling of social phenomena
  4. Unconventional computing based on complex systems
 Professor · Prof. Pilwon Kim
  1. Dynamical systems
  2. Stochastic analysis
  3. Complex networks
  4. Game Theory
Group Members · Graduate student

  • · Soyeong Jeong
  • · Jong-ha Jeon
  • · Jong-o Park

 

Biomathematics Lab
Biomathematics LabWebsite
Research Field Lab Members Mathematical Tools
  1. Biomathematics
  2. Analysis and Computation of Epidemic Models and Reaction Networks
  3. Stochastic Modeling and Computation of Complex Systems
 Professor · Prof. Chang Hyeong Lee
  1. Stochastic processes and stochastic differential equations
  2. ODEs, PDEs and numerical computations
  3. Network analysis based on graph theory
Group Members ·Researcher

· Dr. Jeongeun Kim

 

· Graduate student

  • · Heejun Choi
  • · Minji Lee
  • · Suyeon Kim
Analysis in Nonlinear PDEs group
Analysis in Nonlinear PDEs groupWebsite
Research Field Lab Members Mathematical Tools
Mathematical Analysis of evolution PDEs in fluid dynamics and related equations.

  1. Fluid dynamics: Navier-Stokes equation, Euler equation, Quasi-geostrophic equation
  2. Polymeric fluids
  3. Free boundary problems
  4. Boltzmann equation
  5. Keller-Segel Equation
  6. MHD equation
  7. Hyperbolic conservation Laws
  8. Harmonic analysis
  9. Stability of nonlinear waves
  10. Blow-up analysis
  11. Nonlinear integro-differential equations
  12. Gas dynamics
 Professor · Prof. Bongsuk Kwon
· Prof. Hantaek Bae
· Prof. Kyudong Choi
· Prof. Youngae Lee
  1. Fourier Analysis: Para-differential Calculus, Littlewood-Paley theory
  2. Kinetic formulation
  3. Lagrangian approach
  4. (finite or infinite dimensional) Linear algebra
  5. Classical elliptic PDE theory
Group Members · Dr. Jeongjin Lee
· Graduate student

  • · Hyojung Lee
  • · Ji Heok Kwon
  • · Chan-Ul Kim
  • · Chan-Ul Kim
  • · Yongin ChoiLab Alumni
Number Theory Group
Number Theory Group
Research Field Lab Members Mathematical Tools
Algebraic and analytic number theory with emphasis on Zeta and L-functions

  1. Arithmetic of special values of various zeta functions and L-functions
  2. Analytic properties of various zeta functions and their applications to number fields.
  3. Zeros of various zeta functions and L-functions
  4. Iwasawa theory, p-Adic L-functions of various L-functions and their mu-invariant
 Professor · Prof. Hae-Sang Sun
· Prof. Jaehyun Cho
· Prof. Chol Park
  1. Abstract Algebra
  2. Real and complex analysis
  3. Algebraic geometry
  4. Algebraic topology
  5. Basic harmonic and functional analysis
Group Members · Student

  • · Yohan Kim (Undergrad and Master combined)
  • · Jaesung Kwon (Undergrad))
Computational Mathematical Science Lab
Computational Mathematical Science LabWebsite
Research Field Lab Members Mathematical Tools
  1. Numerical Computation for the differential equations of fractional order
  2. Dynamical Analysis for the fractional systems
  3. BigData Analysis: Traffic, Text Mining
  4. Scientific computation
 Professor · Prof. Bongsoo Jang
  1. Numerical analysis
  2. Scientific computing
Group Members Researcher

  • Dr. Hong-Gyu Yoon
  • Dr. Keerthi Reddy

Graduate Student

  • Junseo Lee
  • Muhammad Ismail
  • Junhyeok Choi
Analysis and computational methods Lab
Analysis and computational methods LabWebsite
Research Field Lab Members Mathematical Tools
Applied analysis, Numerical analysis and methods, Singular perturbation analysis and Uncertainty quantification

  1. Computational methods in applied mathematics
  2. Semi-analytical numerical methods via boundary layer analysis
  3. Uncertainty quantification for stochastic systems
  4. Partial differential equations
 Professor · Prof. Chang-Yeol Jung
  1. Numerical analysis, Scientific computing
  2. Partial differential equations
  3. Singular perturbation Analysis
  4. Probability and statistics
  5. Real analysis
Group Members · Graduate student

  • · Joonho ChoiFormer students
  • · Gong Wonjong (M.S. 2012.06)
  • · Nguyen Thien Binh (M.S. 2012.06, Ph.D. 2015.06)
Mathematical Imaging Lab
Mathematical Imaging LabWebsite
Research Field Lab Members Mathematical Tools
Mathematical Analysis with applications to Image Processing and More

  1. Mathematical Modeling in Image Processing: Image Denoising/Deblurring/Segmentation/Enhancement, etc., Medical/Biomedical Imaging (MRI, CT, EM, etc.)
  2. Computational Aspects of Optimization Problems: Convergence Analysis, Characteristics of Optimal Solutions
  3. Computational Aspects of Eigenvalue Problems in some applications
  4. Phase Retrieval Problem in application to X-ray Crystallography
  5. Deep Learning – Mathematical Analysis
 Professor · Prof. Yunho Kim
  1. Calculus of Variations
  2. PDEs
  3. Real Analysis, Convex Analysis
  4. Probability
  5. Linear Algebra
Group Members · Dr. Dongsun Lee
· Graduate student

  • · Eunji Kim
Mathematical Physics and AI Lab
Mathematical Physics and AI LabWebsite
Research Field Lab Members Mathematical Tools
Mathematical Physics

  1. String Theory
  2. Quantum Field Theories
  3. Supersymmetric Gauge Theories

Machine Learning and Applied Mathematics

  1. Reinforcement Learning, Deep Learning
  2. Optimization, Automation (EDA)
 Professor · Prof. Rak-Kyeong Seong
  1. Representation Theory, Group Theory
  2. Algebraic Geometry, Toric Geometry
  3. Discrete Mathematics, Graph Theory
  4. Combinatorics
Group Members · Graduate student

  • · Minsung Koh (from 2023)