
Search the School of Mathematical SciencesEvents matching "Plurisubharmonic subextensions as envelopes of dis" 
Vertex algebras and variational calculus I 13:10 Fri 4 Jun, 2010 :: School Board Room :: Dr Pedram Hekmati :: University of Adelaide
A basic operation in calculus of variations is the EulerLagrange variational
derivative, whose kernel determines the extremals of functionals. There exists a
natural resolution of this operator, called the variational complex.
In this talk, I shall explain how to use tools from the theory of vertex
algebras
to explicitly construct the variational complex. This also provides a very
convenient language for classifying and constructing integrable Hamiltonian
evolution equations. 

Plurisubharmonic subextensions as envelopes of disc functionals 13:10 Fri 2 Mar, 2012 :: B.20 Ingkarni Wardli :: A/Prof Finnur Larusson :: University of Adelaide
I will describe new joint work with Evgeny Poletsky. We prove a disc formula for the largest plurisubharmonic subextension of an upper semicontinuous function on a domain $W$ in a Stein manifold to a larger domain $X$ under suitable conditions on $W$ and $X$. We introduce a related equivalence relation on the space of analytic discs in $X$ with boundary in $W$. The quotient is a complex manifold with a local biholomorphism to $X$, except it need not be Hausdorff. We use our disc formula to generalise Kiselman's minimum principle. We show that his infimum function is an example of a plurisubharmonic subextension. 

Smooth mapping orbifolds 12:10 Fri 20 May, 2016 :: Eng & Maths EM205 :: David Roberts :: University of Adelaide
It is wellknown that orbifolds can be represented by a special kind of Lie groupoid, namely those that are Ã©tale and proper. Lie groupoids themselves are one way of presenting certain nice differentiable stacks.
In joint work with Ray Vozzo we have constructed a presentation of the mapping stack Hom(disc(M),X), for M a compact manifold and X a differentiable stack, by a FrÃ©chetLie groupoid. This uses an apparently new result in global analysis about the map C^\infty(K_1,Y) \to C^\infty(K_2,Y) induced by restriction along the inclusion K_2 \to K_1, for certain compact K_1,K_2. We apply this to the case of X being an orbifold to show that the mapping stack is an infinitedimensional orbifold groupoid. We also present results about mapping groupoids for bundle gerbes. 

Diffeomorphisms of discs, harmonic spinors and positive scalar curvature 11:10 Fri 17 Mar, 2017 :: Engineering Nth N218 :: Diarmuid Crowley :: University of Melbourne
Media...Let Diff(D^k) be the space of diffeomorphisms of the kdisc fixing the boundary point wise. In this talk I will show for k > 5, that the homotopy groups \pi_*Diff(D^k) have nonzero 8periodic 2torsion detected in real Ktheory. I will then discuss applications for spin manifolds M of dimension 6 or greater: 1) Our results input to arguments of Hitchin which now show that M admits a metric with a harmonic spinor. 2) If nonempty, space of positive scalar curvature metrics on M has nonzero 8periodic 2torsion in its homotopy groups which is detected in real Ktheory. This is part of joint work with Thomas Schick and Wolfgang Steimle. 
Publications matching "Plurisubharmonic subextensions as envelopes of dis"Publications 

Schlicht Envelopes of Holomorphy and Foliations by Lines Larusson, Finnur; Shafikov, R, Journal of Geometric Analysis 19 (373–389) 2009  Dixmier traces as singular symmetric functionals and applications to measurable operators Lord, Steven; Sedaev, A; Sukochev, F, Journal of Functional Analysis 224 (72–106) 2005  ConnesDixmier traces, singular symmetric functionals, and measurable elements in the sense of Connes Lord, Steven; Sedaev, A; Sukochev, F, Mathematical Notes 76 (884–889) 2004  CauchySchwarz functionals Cho, Y; Dragomir, S; Kim, SS; Pearce, Charles, Bulletin of the Australian Mathematical Society 62 (479–491) 2000 
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