Groups and Operator Algebras Seminar

Speaker: Efren Ruiz (University of Hawaii Hilo)

Title: Shift equivalences through the lens of C*-correspondences

Abstract: In a foundational 1973 paper, Williams recast conjugacy and eventual conjugacy problems for shift spaces of finite type purely in terms of equivalence relations between adjacency matrices of directed graphs. These are called Strong Shift Equivalence (SSE) and Shift Equivalence (SE), respectively. It was shown by Kim and Roush that shift equivalence is decidable, but the problem of decidability of SSE remains a fundamental open problem in symbolic dynamics. Thus finding different formulations of SSE may help in resolving the decidability. In this talks, I will introduce several “shift equivalences” of matrices using C*-correspondences and show which of these are known to be the same as SSE.

GOA website: https://sites.google.com/view/copenhagen-goa-seminar