**Title:** Expander phenomena for Bohr sets

**Speaker:** Professor Alexander Fish

**Speaker Info:** Ohio State

**Brief Description:**

**Special Note**:

**Abstract:**

Let B be a Bohr set {n in Z | n \alpha in U}, where \alpha \in T^d is such that the orbit closure of zero by action R_{\alpha}(x) = x + \alpha in T^d is connected, U is an open box in T^d. Then we establish the following results:1) d^{*}(B+S) \geq min(1, d^{*}(B) + d^{*}(S)) (d^{*} - denotes for upper Banach density)

2) in the case of an equality in (1): a) B is one-dimensional (B can be represented up to upper density zero as return times of zero to an interval under irrational rotation on one-dimensional torus) b) S is PW-Bohr with the interval in the definition of Bohr has the length d^{*}(S) and the rotation is by the same \alpha, as in B.

Joint work with M.Bjorklund from KTH (Sweden).

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