Algebraic positivity and property (T)

Speaker(s)

Marek Kaluba

Affiliation

UAM

Date

April 5, 2022, 4:30 p.m.

Information about the event

4070 oraz Zoom: 892 1108 9551 Password - type the number equal to rk(H^2((S^1)^{200};Z))

Seminar

Seminar Algebraic Topology

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Property (T) for a group G is originally defined in terms of all unitary representations on Hilbert spaces. I will show how to use Positivstellensätze in group rings to reduce property (T) to a specific algebraic question RG in the group ring. Then I will define grading of group by root system and show how it may be used to prove property (T) for whole families of groups with compatible gradings by solving a single equation in the group ring. A specific example of such application is the result that Aut(Fₙ) has property (T) for n ≥ 6.

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