The Computability of Some Problems in Borel Combinatorics

Explore the computability aspects of Borel combinatorics problems through this 44-minute conference talk that examines the existence of Borel equivariant maps from Bernoulli shifts to subshifts of finite type. Focus on cases where the acting group is a finitely generated free abelian group, discovering that one-dimensional problems are computable while two-dimensional continuous problems achieve c.e.-completeness. Gain insights into the intersection of computability theory and Borel combinatorics, understanding how dimensional complexity affects computational tractability in these mathematical structures. Learn about the theoretical foundations connecting reverse mathematics, higher computability theory, and combinatorial problems in Borel spaces.