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Logic Seminar

Monday, June 21, 2021
12:00pm to 1:00pm
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Online Event
Local entropy and descriptive complexity
Udayan Darji, Department of Mathematics, University of Louisville,

Blanchard introduced the concepts of Uniform Positive Entropy (UPE) and Complete Positive Entropy (CPE) as topological analogues of K-automorphism. He showed that UPE implies CPE, and that the converse is false. A flurry of recent activity studies the relationship between these two notions. For example, one can assign a countable ordinal which measures how complicated a CPE system is. Recently, Barbieri and García-Ramos constructed Cantor CPE systems at every level of CPE. Westrick showed that natural rank associated to CPE systems is actually a Π11-rank. More importantly, she showed that the collection of CPE Z2-SFT's is a Π11-complete set. In this talk, we discuss some results, where UPE and CPE coincide and others where we show that the complexity of certain classes of CPE systems is Π11-complete. This is joint work with García-Ramos.

For more information, please email A. Kechris at [email protected].