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SUMMARY:The Slice theorem and the Reduction theorem
DTSTART:20260224T131500Z
DTEND:20260224T150000Z
DTSTAMP:20260308T043600Z
UID:indico-event-1108@math-events.uni-bonn.de
DESCRIPTION:Speakers: Christian Carrick\n\nI will give six lectures on the
  Hill—Hopkins—Ravenel solution to\nthe Kervaire invariant one problem.
  I will attempt to emphasize two key\npoints that don’t feature prominen
 tly in their article. The first is the\nstudy of higher real K-theories: t
 hese are the fixed points of Morava\nE-theories with respect to finite sub
 groups of the Morava stabilizer\ngroup. Hill—Hopkins—Ravenel set out t
 o understand the homotopy fixed point\nspectral sequences (HFPSS) of highe
 r real K-theories\, and they proved a\nnumber of results on the action of 
 finite groups on Lubin—Tate spaces and\non differentials in the HFPSS th
 at have not appeared fully in print. These\nresults beautifully inspired t
 heir detour through Real-oriented homotopy\ntheory\, which removed the nee
 d for higher real K-theories in their\nsolution altogether.\n\nThe second 
 point concerns the technical foundations of genuine equivariant\nhomotopy 
 theory needed in their solution. The work of Hill—Hopkins—Ravenel\nins
 pired a renaissance in the foundations of equivariant and parametrized\nho
 motopy theory\, and their norm functor gave rise to the study of\nparametr
 ized monoidal structures. I will attempt to revisit their work\nfrom the p
 oint of view of these developments. I will finish the course by\ndiscussin
 g developments in Real-oriented homotopy theory following\nHill--Hopkins--
 Ravenel. Their detour through Real-oriented homotopy can be\nseen as provi
 ding good connective models of higher real K-theories\, and\nthe study of 
 these connective models - especially through the slice\nspectral sequence 
 of Hill--Hopkins--Ravenel - has brought about an\nexplosion of progress in
  chromatic homotopy theory at the prime 2. I will\ndiscuss this progress a
 s well as future directions and possibilities at\nodd primes.\n\nhttps://m
 ath-events.uni-bonn.de/event/1108/
LOCATION:Endenicher Allee 60/0-008 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1108/
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