BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Naomi Andrew (Oxford) DTSTART:20250626T123000Z DTEND:20250626T133000Z DTSTAMP:20260423T003231Z UID:GaTO/121 DESCRIPTION:Title: T he Farrell--Tate K-theory of $\\mathrm{Out}(F_n)$\nby Naomi Andrew (Ox ford) as part of Geometry and topology online\n\nLecture held in Room B3.0 2 in the Zeeman Building\, University of Warwick.\n\nAbstract\nGiven a (ni ce enough) group\, there is an isomorphism\, due to Lück\, relating the r ationalised K-theory groups of its classifying space to a large product of cohomology groups\, some with rational and some with $p$-adic coefficient s.\n\nWe identify a generalised cohomology theory capturing the $p$-adic p art of this product. Working in $\\mathrm{Out}(F_n)$\, in ranks close to $ p$ we can fully compute this $p$-adic part and in this way produce an infi nite family of odd-dimensional summands in the rationalised K-theory of $\ \mathrm{Out}(F_n)$. I will discuss these results and the tools that go in to them\, which range from spherical group rings to the lemma that is not Burnside's\, via results about centralisers in $\\mathrm{Out}(F_n)$: I wil l try to explain how all these various ideas fit together!\n\nThis is join t work with Irakli Patchkoria.\n LOCATION:https://researchseminars.org/talk/GaTO/121/ END:VEVENT END:VCALENDAR