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
      • c-numerical range
      • joint numerical range
      • rank-k-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
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  • 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

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