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Periodicities of higher real $K$-theories

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EHTW03 - New horizons for equivariance in homotopy theory

Historically, topological $K$-theory and its Bott periodicity have been very useful in solving key problems in algebraic and geometric topology. In this talk, we will explore the periodicities of higher real $K$-theories and their roles in several contexts, including Hill—Hopkins—Ravenel’s solution of the Kervaire invariant one problem. We will prove periodicity theorems for higher real $K$-theories at the prime 2 and show how these results feed into equivariant computations. We will then use these periodicities to measure the complexity of the $RO(G)$-graded homotopy groups of Lubin—Tate theories and to compute their equivariant slice spectral sequences. This is joint work with Zhipeng Duan, Mike Hill, Guchuan Li, Yutao Liu, Guozhen Wang, and Zhouli Xu.

This talk is part of the Isaac Newton Institute Seminar Series series.

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