Research Groups

In order to assist and inform our Mathematics students, we have instituted a set of research groups. These groups meet for regular seminars, and are comprised of faculty members and graduate students.

Nonlinear Complex Systems Lab   http://math.unist.ac.kr/~pwkim

1. Research Field : 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

2. Group Members

3. Mathematical Tools

  • 1)  Dynamical systems
  • 2)  Stochastic analysis
  • 3)  Complex networks
  • 4)  Game Theory

Stochastic Analysis and Simulation Lab   http://biomath.unist.ac.kr

1. Research Field :

  • 1)  Biomathematics
  • 2)  Analysis and Computation of Epidemic Models and Reaction Networks
  • 3)  Stochastic Modeling and Computation of Complex Systems

2. Group Members

3. Mathematical Tools

  • 1)  Stochastic processes and stochastic differential equations
  • 2)  ODEs, PDEs and numerical computations
  • 3)  Network analysis based on graph theory

Analysis in Nonlinear PDEs group

1. Research Field : Mathematical Analysis of evolution PDEs in fluid dynamics and related equations.

  • Fluid dynamics: Navier-Stokes equation, Euler equation, Quasi-geostrophic equation
  • Polymeric fluids
  • Free boundary problems
  • Boltzmann equation
  • Keller-Segel Equation
  • MHD equation
  • Hyperbolic conservation Laws
  • Harmonic analysis
  • Stability of nonlinear waves
  • Blow-up analysis
  • Nonlinear integro-differential equations
  • Gas dynamics

2. Group Members

3. Mathematical Tools

  • Fourier Analysis: Para-differential Calculus, Littlewood-Paley theory
  • Kinetic formulation
  • Lagrangian approach
  • (finite or infinite dimensional) Linear algebra
  • Classical elliptic PDE theory

Computational Mathematical Science Lab   http://amath.unist.ac.kr

1. Research Field

  • 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

2. Group Members

3. Mathematical Tools

  • Numerical analysis
  • Scientific computing

Number Theory Group

1. Research Field : 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

2. Group Members

  • Prof. Hae-Sang Sun http://www.math.unist.ac.kr/~haesang
  • Prof. Jaehyun Cho
  • (visiting) Prof. Byungheup Jun
  • (visiting) Prof. Myoungil Kim
  • Student:
    • Yohan Kim (Undergrad and Master combined)
    • Jaesung Kwon (Undergrad)

3. Mathematical Tools

  • 1)  Abstract Algebra
  • 2)  Real and complex analysis
  • 3)  Algebraic geometry
  • 4)  Algebraic topology
  • 5)  Basic harmonic and functional analysis

Analysis and computational methods Lab   http://jung.unist.ac.kr

1. Research Field : 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

2. Group Members

3. Mathematical Tools

  • 1)  Numerical analysis, Scientific computing
  • 2)  Partial differential equations
  • 3)  Singular perturbation Analysis
  • 4)  Probability and statistics
  • 5)  Real analysis

Mathematical Imaging Lab   http://yunhokim.wordpress.com

1. Research Field : 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

2. Group Members

3. Mathematical Tools

  • 1)  Calculus of Variations
  • 2)  PDEs
  • 3)  Real Analysis, Convex Analysis
  • 4)  Probability
  • 5)  Linear Algebra