Operator algebras,non-commutative geometry

Non commutative geometry is a research field that intersects algebra and geometry. originating in the late 1940s when people sought quantum geometry by developing the quantization of spacetime. This discipline studies the structural characteristics of non commutative algebra and non commutative topological spaces, constructs a mathematical framework based on quantum commutation rules, and develops new directions such as non commutative topology and calculus. lts theoretical system covers core contents such as non commutative algebra, non commutative topology geometric analysis, etc.lts research scope includes K theory, exponential theorem and semi classical analysis problems on quantum torus.