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Events on Friday 31 March 2017

Geometric structures on moduli spaces
12:10 Fri 31 Mar, 2017 :: Napier 209 :: Nicholas Buchdahl :: University of Adelaide

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Moduli spaces are used to classify various kinds of objects, often arising from solutions of certain differential equations on manifolds; for example, the complex structures on a compact surface or the anti-self-dual Yang-Mills equations on an oriented smooth 4-manifold. Sometimes these moduli spaces carry important information about the underlying manifold, manifested most clearly in the results of Donaldson and others on the topology of smooth 4-manifolds. It is also the case that these moduli spaces themselves carry interesting geometric structures; for example, the Weil-Petersson metric on moduli spaces of compact Riemann surfaces, exploited to great effect by Maryam Mirzakhani. In this talk, I shall elaborate on the theme of geometric structures on moduli spaces, with particular focus on some recent-ish work done in conjunction with Georg Schumacher.
One-layer liquid films loaded with self-propelled particles and two-layer films under vibration
15:10 Fri 31 Mar, 2017 :: Engineering South S111 :: Dr Andriy Pototskyy :: Swinburne University of Technology

In the first part, we consider a colony of self-propelled particles (swimmers) in a thin liquid film resting on a solid plate with deformable liquid-gas interface. The local surface tension of the liquid-gas interface is altered by the local density of swimmers due to the soluto-Marangoni effect. Linear stability of the flat film and nonlinear time evolution is analyzed in case of the swarming interaction between the swimmers. In the second part, we study the Faraday instability and nonlinear patterns in vibrated two-layer liquid films. For gravitationally stable two-layer films with a lighter fluid on top of the heavier fluid, we find squares, hexagons, quasiperiodic patterns with eightfold symmetry as well as localized states in the form of large scale depletion regions or finite depth holes, occurring at the interface and surface. For a Rayleigh-Taylor unstable combination (heavier fluid above the light one) we show that external vibration increases the lifetime of the film by delaying or completely suppressing the film rupture.
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