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Monday, November 13, 2017

**Abstract:** In their attempt to find a better qualitative understanding of the stable homotopy groups of spheres, Morava and Miller-Ravenel-Wilson found that there are pervasive periodic phenomena in the Adams-Novikov E_2-term. These phenomena were originally understood only algebraically, but in 1984, Doug Ravenel attempted to provide topological origins for these algebraic periodicities. He asked, the now famous, telescope conjecture, which in essence, asks to what degree the topological periodic phenomena is controlled by the geometry of formal groups. In this talk, I will give a precise formulation of the telescope conjecture and sketch Miller’s proof of the height 1 telescope conjecture at odd primes. I will also sketch the basic ideas of chromatic homotopy theory along the way.