My current research interests include matrix and combinatorial theory. I am in particular interested in problems in numerical range, sign pattern matrices, number of independent sets, and their applications.

• Numerical range
  • Geometric properties
    • Characterize a matrix to have circular or elliptic numerical range
    • Parametricize the boundary curve of the c-numerical range via enveolping method and elliptic curve theory
    • Elliptic curves arising in numerical range
    • Poncelet property
  • Higher numerical range
    • q-numerical range
    • linear pencil
    • matrix polynomial
  • Special matrices
    • Classical and c-numerical range of tridiagonal matirces
    • c-numerical range of generalized circulant matrices
    • Numerical range of a continuant matrix
    • c-numerical range of a rank one matrix
  • Algorithms
    • Plotting c-numerical range
    • Numerical area of c-numerical range
  • Applications
    • Positiveness of a tridiagonal matrix
    • Bounds for for zeros of a ploynomial

    　

• Sign pattern matrices
  • Require a specific property
  • Allow a specific property

• Number of independent sets of a graph
  • Independent sets of a graph
  • Independ edge of a graph