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Research Areas

Our department is dedicated to advancing the frontiers of mathematical knowledge through rigorous research in operator theory, harmonic analysis, and noncommutative geometry.

Operator Algebras & Noncommutative Geometry

Research in this area focuses on the structure and classification of operator algebras, subfactors, and their applications in quantum theory.

Core Topics

  • Inclusions of $C^*$-algebras and von Neumann algebras
  • Subfactors and Finite Watatani Index
  • Planar Algebras (Spin, Intermediate, and Latin Square types)
  • Quantum Information Theory and Quantum Symmetry
  • KMS States on $C^*$-algebraic structures
  • Fourier-theoretic inequalities for $C^*$-algebra inclusions

Representative Publications

"Higher reflections and entropy of canonical shifts for inclusions of $C^*$-algebras with finite Watatani index"

"Noncommutative BKW-operators"

"KMS states on $C_c^*(\mathbb{N}^2)$"

Harmonic Analysis & Geometric Inequalities

Exploring fundamental inequalities and their applications in various geometric and functional settings.

Core Topics

  • Hardy-Littlewood-Sobolev inequalities on upper half spaces
  • Analysis on Dunkl settings and Dunkl operators
  • Fractional Hardy and Sobolev inequalities
  • Existence of extremals for Dunkl-type inequalities
  • Stein-Weiss inequalities for Dunkl Riesz potentials
  • Trace Hardy inequalities for Dunkl gradients

Representative Publications

"Hardy-Littlewood-Sobolev inequality for upper half space"

"Improved fractional Hardy inequalities for Dunkl gradient"

"Existence of extremals of Dunkl-type Sobolev inequality"