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Events 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 Euler-Lagrange 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
to explicitly construct the variational complex. This also provides a very
convenient language for classifying and constructing integrable Hamiltonian
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 well-known 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©chet-Lie 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 infinite-dimensional 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
Let Diff(D^k) be the space of diffeomorphisms of the k-disc fixing the boundary point wise. In this talk I will show for k > 5, that the homotopy groups \pi_*Diff(D^k) have non-zero 8-periodic 2-torsion detected in real K-theory. 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 non-empty, space of positive scalar curvature metrics on M has non-zero 8-periodic 2-torsion in its homotopy groups which is detected in real K-theory. This is part of joint work with Thomas Schick and Wolfgang Steimle.
Publications matching "Plurisubharmonic subextensions as envelopes of dis"
|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
|Connes-Dixmier traces, singular symmetric functionals, and measurable elements in the sense of Connes|
Lord, Steven; Sedaev, A; Sukochev, F, Mathematical Notes 76 (884–889) 2004
Cho, Y; Dragomir, S; Kim, S-S; Pearce, Charles, Bulletin of the Australian Mathematical Society 62 (479–491) 2000
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