**SMS scnews item created by Haotian Wu at Fri 7 Apr 2017 2039**

Type: Seminar

Distribution: World

Expiry: 7 Oct 2017

**Calendar1: 13 Apr 2017 1200-1300**

**CalLoc1: Carslaw 535A**

CalTitle1: Geometry & Topology Seminar: Diarmuid Crowley -- Diffeomorphisms of discs and positive scalar curvature

Auth: haotianw@como.maths.usyd.edu.au

### Geometry & Topology Seminar

# Diffeomorphisms of discs and positive scalar curvature

### Diarmuid Crowley (Melbourne)

**Thursday 13 Apr 12:00–13:00 in Carslaw 535A.**

Please join us for lunch after the talk!

**Abstract:**
Let \({\rm Diff}(D^k)\) be the space of diffeomorphisms of the \(k\)-disc fixing the boundary pointwise. Understanding the topology of \({\rm Diff}(D^k)\) is a longstanding and difficult problem in differential topology. In this talk I will report on recent work with Thomas Schick and Wolfgang Steimle which shows that for \(k > 5\) the homotopy groups \(\pi_* {\rm Diff}(D^k)\) have non-zero \(8\)-periodic \(2\)-torsion detected in real K-theory. I will then discuss applications to the space of positive scalar curvature metrics on spin manifolds of dimension \(6\) or greater.

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