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SUMMARY:Motivic Hochschild and cyclic homology - Bjørn Dundas (Universite
 tet i Bergen)
DTSTART:20250506T143000Z
DTEND:20250506T153000Z
UID:TALK230449@talks.cam.ac.uk
DESCRIPTION:Ongoing work joint with Paul Arne &Oslash\;stv&aelig\;r.\nMoti
 vic calculations sometimes facilitate calculations in topology and sometim
 es they shed light on relations that initially appear mysterious. The calc
 ulations of motivic Hochschild homology (MHH) of low chromatic height have
  mostly been of the latter type\, where a lot of zeros in topology have ap
 peared as torsion. The torsion is due to the tension between the topologic
 al circle and G_m\, which I may comment on if time permits\, but the main 
 message in this talk is that the torsion actually holds valuable informati
 on. Indeed\, climbing up the chromatic tower to cobordism we find that the
  torsion classes are placeholders for non-torsion in MHH(MGL). Equivariant
 ly\, however\, torsion reappears.\n&nbsp\;\nIn this talk I plan to outline
  yet another approach to the K-theory K(MU)\, or rather TC(MU)\, by workin
 g motivically over the complex numbers\, which potentially can compete or 
 work in tandem with existing approaches (some of which use the word &ldquo
 \;motivic&rdquo\; in a different sense).
LOCATION:Seminar Room 2\, Newton Institute
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