Dynamical Systems Seminar | Andreas Mountakis (Northwestern University)

Title: Recurrence for pretentious systems along generalized Pythagorean
triples

Abstract: We establish multiple recurrence results for pretentious measure-preserving
multiplicative actions along generalized Pythagorean triples, that is, solutions to the
equation $ax^2 + by^2 = cz^2$. This confirms the ergodic-theoretic form of the generalized
Pythagorean partition regularity conjecture in this critical case of structured measure-preserving actions. This is based on joint work with Nikos Frantzikinakis.

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