Noncommutative geometry, at its core, challenges the classical notion of a point by allowing coordinates to fail to commute. This alteration leads to a rich interplay between geometry and algebra, ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of recent work by the ...

Hopf algebras amalgamate the structures of both algebras and coalgebras, incorporating a multiplicative framework alongside comultiplication and an antipode that serve to intertwine these dual aspects ...