Aditya Thorat, International Centre for Theoretical Sciences, Bengaluru

Title: Finitely dependent processes on Z^d subshifts.

Abstract: Finitely dependent processes are a generalisation of independent processes which require only that restrictions of the process to sufficiently separated subsets of Z^d are independent. Schramm, Holroyd and Wilson showed that there are no stationary finitely dependent processes on proper 3-colorings of Z^d for d>1. But Holroyd and Liggett proved that there are stationary finitely dependent processes on proper 4-colorings of Z^d for any d. Proper q-colorings of Z^d are examples of
so-called subshifts. We will discuss some results addressing the following question: When do subshifts support finitely dependent processes? We will see how cocycles (a.k.a. height functions) on subshifts can be used to answer this question in certain classes of subshifts, including tiling spaces by a collection of rectangles in plane. 

This is joint work with Nishant Chandgotia, Jan Grebík, and Filip Kučerák.