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Tuesday, September 12, 2017

**Abstract:** In the 1980s Mahowald and Mahowald-Lellmann studied the Adams spectral sequence for the sphere based on the connective real K-theory spectrum. In particular, it was used to study the height 1 telescope conjecture at the prime 2 and to perform low dimensional calculations of the stable homotopy groups of the sphere. Motivated by this, Mahowald proposed using the connective spectrum of topological modular forms to study height 2 telescope phenomena and to perform calculations. This requires understanding the cooperations algebra for tmf, and work of Behrens, Ormsby, Stapleton, and Stojanoska give partial calculations of this cooperations algebra. In this talk, I will talk discuss the problem of computing the cooperations algebra for a variant of tmf, which is sometimes referred to as BP<2>.