Symbolic Dynamics and Graph Algebras

Time: 10:45 - 11:45, October 28, 2026

Venue: Room 612, A6, Institute of Mathematics-VAST

Abstract: Symbolic dynamics provides simple yet surprisingly rich models for dynamical systems, though many fundamental classification problems remain unresolved. A central example is the conjugacy problem for subshifts of finite type (SFTs), whose complexity is reflected in deep links to combinatorics and matrix theory. Building on the seminal work of Cuntz and Krieger, one can associate graph C*-algebras and Leavitt path algebras to SFTs in a way that recovers classical invariants of the dynamics, while also producing new algebraic obstructions to conjugacy. In this talk, I will present recent advances in understanding the relationship between symbolic dynamics and graph algebras, including a resolution of Hazrat's graded classification conjectures, which we refute by way of showing that conjugacy of SFTs coincides with graded Morita equivalence of the associated Leavitt path algebras. These results illustrate how graph algebras, in both the analytic and purely algebraic settings, not only encapsulate longstanding problems in symbolic dynamics but also open new avenues at the interface of functional analysis, pure algebra, and quantum mathematics.