Title
Evolution algebras and evolution coalgebras: a dynamical systems perspective
Abstract
In this talk, I will introduce evolution algebras and the newly defined evolution coalgebras. Evolution algebras are non-associative, while evolution coalgebras are in general neither cocommutative nor coassociative. Both structures exhibit interesting properties and admit natural interpretations in terms of dynamical systems and stochastic processes, with potential applications to quantum probability theory. To provide a coherent picture, I will begin with basic notions of algebras, coalgebras, bialgebras, and Hopf algebras, and then explain how they relate to dynamical systems. No proofs will be given, and the talk will be accessible to graduate students; advanced undergraduate students are also encouraged to attend.