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SUMMARY:Periodicities of higher real $K$-theories - XiaoLin Danny Shi (Uni
 versity of Washington)
DTSTART:20250516T104500Z
DTEND:20250516T114500Z
UID:TALK230560@talks.cam.ac.uk
DESCRIPTION: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&rsquo\;s solution of the Kervaire invariant one problem. We will
  prove periodicity theorems for higher real $K$-theories at the prime 2 an
 d show how these results feed into equivariant computations. We will then 
 use these periodicities to measure the complexity of the $RO(G)$-graded ho
 motopy groups of Lubin--Tate theories and to compute their equivariant sli
 ce spectral sequences. This is joint work with Zhipeng Duan\, Mike Hill\, 
 Guchuan Li\, Yutao Liu\, Guozhen Wang\, and Zhouli Xu.
LOCATION:Seminar Room 1\, Newton Institute
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