# Gap Phenomenon for Some Interval Maps

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Diaaeldin Taha, University of Washington
Fine Hall 401

The three gap theorem states that for any integer $N$ and real number $\alpha$ there are at most three distinct gap lengths in the fractional parts of the sequence $\alpha, 2\alpha, \cdot, N\alpha$. In this talk, we review this classic theorem along with several of its recent generalizations to orbits of some interval maps. We also review methods that have been introduced to derive average gap distributions related to the aforementioned gap theorems.