We show that there is a homotopy cofiber sequence of spectra relating Carlsson’s deformation K-theory of a group G to its “deformation representation ring,” analogous to the Bott periodicity sequence… (More)

We calculate the integral homotopy groups of THH ( ) at any prime and of THH (ko) at p = 2, where is the Adams summand of the connective complex p-local K-theory spectrum and ko is the connective… (More)

For finitely generated groups G and H, we prove that there is a weak equivalence KG∧ku KH ' K(G × H) of ku-algebra spectra, where K denotes the “unitary deformation K-theory” functor. Additionally,… (More)

Elevated seawater pCO2, and in turn ocean acidification (OA), is now widely acknowledged to reduce calcification and growth of reef building corals. As with other environmental factors (e.g.,… (More)

We apply a theorem of J. Lurie to produce cohomology theories associated to certain Shimura varieties of type U(1, n−1). These cohomology theories of topological automorphic forms (TAF ) are related… (More)

An algebraic criterion, in terms of closure under power operations, is determined for the existence and uniqueness of generalized truncated Brown-Peterson spectra of height 2 as E∞-ring spectra. The… (More)

Previous work constructed a generalized truncated Brown-Peterson spectrum of chromatic height 2 at the prime 2 as an E∞-ring spectrum, based on the study of elliptic curves with level-3 structure. We… (More)

Let S2 be the p-primary second Morava stabilizer group, C a supersingular elliptic curve over Fp, O the ring of endomorphisms of C, and l a topological generator of Z×p (respectively Z × 2 /{±1} if p… (More)

The cohomology theory known as Tmf, for “topological modular forms,” is a universal object mapping out to elliptic cohomology theories, and its coefficient ring is closely connected to the classical… (More)

We show that the free E∞-algebra on a zero-cell cannot be modeled by a commutative Γ-ring. The proof shows that DyerLashof operations of positive degree must vanish on the zero’th homology of such an… (More)