The algebraic K-theory of the sphere spectrum, the geometry of high-dimensional manifolds, and arithmetic


Andrew Blumberg

UT Austin

Northeastern University

Thursday, November 10, 2016


Talk at 4:30 p.m. in 509 Lake Hall

Tea at 4:00 p.m. in 553 Lake Hall


Abstract: Quillen's higher algebraic K-theory, applied to number fields, captures information about the zeta function and L-functions. Waldhausen's generalization of K-theory to ring spectra (multiplicative cohomology theories), applied to the "spherical group ring" on the based loops of a manifold, captures information about differential topology. In particular, K(S), the algebraic K-theory of the sphere spectrum (corresponding to the cohomology theory stable cohomotopy theory), encodes information about BDiff of highly-connected high dimensional manifolds. This talk explains on-going work with Mike Mandell that describes K(S) in terms of arithmetic duality.

Here are some directions to Northeastern University. Lake Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street.

There is free parking available for people coming to the Colloquium at Northeastern's visitor parking (Rennaisance Garage). The entrance is from Columbus Avenue. If coming by car, you should park there and take the parking talon. After the lecture, you may pick up the payment coupon from one of NEU colloquium organizers.

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Posted: November 10, 2016    URL: