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Tuesday, February 8, 2005

**Abstract:** I will define Hochschild cohomology and topological Hochschild cohomology as derived functors of the center, and give some examples. Baker and Lazarev have shown that THH(KU/2)=KU_2, 2-completed K-theory. I will explain this result, and how it continues to hold at odd primes, if we equip KU/p with a non-commutative multiplication. If we instead consider THH(K(1)), I will try to argue that we get E(1)^[a]/(p=a^(p-1)v_1), i.e., the completed Johnson-Wilson spectrum adjoined a (p-1)st root of pv_1^-1, though this is still work in progress.