BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dustin Clausen (Max Plank Institute) DTSTART:20200728T160000Z DTEND:20200728T170000Z DTSTAMP:20260423T004140Z UID:MITTop/7 DESCRIPTION:Title: T he Linearization Hypothesis\nby Dustin Clausen (Max Plank Institute) a s part of MIT topology seminar\n\n\nAbstract\nLazard showed that the conti nuous group cohomology of a large class ofp-adic Lie groups\, with p-adic coefficients\, satisfies Poincare duality. Analogously to the usual Poinca re duality of real manifolds\, there are orientability issues\, but Lazard showed that the relevant orientation local system is completely determine d by the adjoint representation of the group in an explicit manner\, allow ing for an easy analysis. This can be compared to how the orientation loc al system on a real manifold is determined by the tangent bundle\, a very useful "linearization" of the problem. Now\, there is an analogous Poinca re duality with spectrum coefficients both in the setting of p-adic Lie gr oups and in the setting of real manifolds. In the latter case the relevan t orientation local system is still determined by the tangent bundle\; in fact it is the suspension spectrum of the associated sphere bundle\, a sta tement known as Atiyah duality. In the former case\, there is a natural g uess for how the orientation local system should still be determined by th e adjoint representation. This has been highlighted by recent work of Bea udry-Goerss-Hopkins-Stojanoska in their study of duality for tmf\, and the y dubbed this guess the "linearization hypothesis". Neither Lazard's tech niques nor the usual arguments for Atiyah duality can be used to attack th e\nlinearization hypothesis. In this talk I will explain a proof of the l inearization hypothesis\, whose main ingredients are a deformation of any p-adic Lie group to its Lie algebra\, and a rather exotic "cospecializatio n map" which lets you use this deformation to jump from the Lie algebra to the Lie group as if the deformation were parametrized by a unit interval\ , even though it is only parametrized by a totally disconnected space.\n LOCATION:https://researchseminars.org/talk/MITTop/7/ END:VEVENT END:VCALENDAR