- Geometry of Dixmier-Douady Class
- Classical Theory of Fourier Series
- Spectrum and Primitive Ideal Space
- Symplectic Groupoid
- Continous Trace C*-Algebras
- Abelian Sheaf Cohomology
- Grothendieck Topology
- Sheaf and Presheaf
- Dixmier-Douady Theory
- Equivariant Brauer Group of C*-Dynamical Systems
- The Algebra of Compact Operators
- Strong Morita Equivalence
- The Stone Von-Neumann Theorem
- Multiplier Algebra
- Transformation Group
- Pontrjagin Duality
- Geometric Langlands
- Geometric Quantization
- Gelfand Theory
- Representation Theory in 2-Categories
- Orbital Integrals
- Dirac Geometry
- Poisson-Lie Group, Lie bialgebra and Manin triple
- $s$-density Bundle
- Integral Transforms
- Tensor Categories
- Differentiable Stack
- Guillemin-Sternberg Conjecture
- Coadjoint Orbit
- Isbell Duality
- Automorphic Forms
- Abstract Harmonic Analysis
- Quantization
- Geometric Representation Theory
- Index Theory
- KK-Theory
- Noncommutative Geometry
- Topos Theory
- Generalized Spaces
- Stacks and Gerbes
- Higher Geometry
- Fourier-Mukai Duality
- Baum-Connes Conjecture
- Diffeological Space
- Siegel Modular Forms
- Momentum in Diffeology
- The Orbit Method
- Central $U(1)$-Extensions
- Quantum Logic
- von Neumann Algebra
- Category Theory
- Poisson Geometry
- Bundle Gerbes
- Theta Function
- Heisenberg Algebra and Heisenberg Group
- Algebraic Theory
- Geometric Theory
- Fourier Integral Operators
- Weyl Quantization
- Deformation Quantization
- Classical Mechanics from Quantum Mechanics
- Morita Equivalence
- Hamiltonian Group Action
- Chern-Weil Theory
- Yoneda Lemma
- Split Orthogonal Group
- Noncommutative Torus
- Crossed Product C*-algebra