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Mathematics Colloquium


Date:  Tuesday, January 11, 2011

Title:  Homotopy and Reality

Abstract:  The operation of complex conjugation, and its generalizations, have played a surprisingly prominent role in homotopy theory. Atiyah's famous 1966 paper ``K-theory and Reality'' started a series of developments which included my work with Hu on Real cobordism, and culminated in the recent solution of the Kervaire invariant 1 problem by Hill, Hopkins and Ravenel. It turns out, however, that many properties of the complex projective line associated with complex conjugation are shared by the projective line over any field, regardless of existence of quadratic extensions. This plays an important role in Voevodsky's motivic homotopy theory, and his solution of the Milnor and Bloch-Kato conjectures. Both contexts come together in the notion of Hermitian K-theory, and my recent joint work with Hu and Ormsby on Thomason's homotopy limit problem. I will explain some of this in my talk.

Speaker:  Igor Kriz
Institution:  University of Michigan


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