Congratulations to Colin Little for passing his PhD viva on Friday 1st March.  The title of his PhD thesis is “Deterministic driven random walks in a random environment“, and the project was supervised by Ian Melbourne.  The external examiner was Mark Holland (Exeter University) and the internal examiner was Claudia Wulff.

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Michelle Grant started as PhD student at Surrey in January 2013. Her project will focus on data assimilation in systems with multiple scales under the supervision of Anne Skeldon and Ian Roulstone.

Michelle graduated with a mathematics degree from Edinburgh University in 2000 and moved into the financial sector, predominantly employed in Corporate Treasury roles.  This has encompassed interest rate risk management, own-asset securitisation, and a considerable amount of risk modelling at RBS Group Treasury, Lloyds Corporate Markets and Santander Global Banking and Markets.

Her PhD project is linked to the inter-departmental Evolution and Resilience of Industrial Ecosystems (ERIE) project, and Michelle is based with the ERIE team, where she hopes to be able to apply data assimilation methods to some of the case study models being developed within the ERIE project

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Kostas Sfetsos is visited Imperial College on Wednesday 27 February to give a talk in the London Triangle String Theory Seminar series.  The title of his talk is “Non-abelian T-duality in supergravity and the AdS/CFT correspondence” with abstract as follows.  The notion of T-duality in supergravity backgrounds with non-Abelian isometries and non-vanishing RR fluxes will be explained. The talk will then focus on type-II backgrounds on which the duality action preserves supersymmetry. For the case of D3-branes at the tip of the conifold dualising along an SU(2) isometry provides a type-IIA background with M-theory lift is of the type describing duals to certain N=1 SCFT quivers produced by M5-branes wrapping a Riemann surface. In the non-conformal cases we find smooth duals in massive IIA supergravity with a Romans mass naturally quantized.  The interpretation of these geometries in the context of the AdS/CFT correspondence is initiated and the fate of various charges under dualisation is discussed. The backgrounds suggest a form of Seiberg duality in the dual field theories which also exhibit domain walls and confinement in the infrared.

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Tom Bridges gave at talk in the Dynamical Systems Seminar at Imperial College on Thursday 28 February.  The title of the talk is “How modulation generates geometry in dynamical systems and nonlinear waves“.  An abstract of the talk follows.  The backbone of the talk is “modulation”; specifically what to modulate and how modulation generates geometry.  The talk is based on three examples.  (1D modulation) how modulation gives a new viewpoint on elementary homoclinic bifurcation with curvature of modulation determining the coefficient of the nonlinear term.  (2D modulation) the mythical origins of the KdV equation are given a new perspective, resulting in a universal form for emergence and how geometry of modulation determines the coefficients, and a dynamical systems argument determines the dispersion. Considering that the classical derivation of KdV is about the trivial solution, a by-product of the result is how to modulate the trivial solution!  (3D modulation) The third example will show how modulation of periodic solutions leads to a sequence of multi-pulse planforms in PDEs like the Swift-Hohenberg equation.  This theory is deduced by deriving a new modulation equation in two space dimensions and time.

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Sara Pasquetti visited the Theoretical Physics group at the Universita degli Studi de Milano-Bicocca.  During the visit she gave a seminar on Friday 22 February in the TP seminar.  The title is “Holomorphic blocks in three dimensions“.  In the talk it is shown that sphere partition functions and indices of 3 dimensional N=2 gauge theories can be decomposed into a sum of products of a universal set of holomorphic blocks. The blocks count BPS states of a theory on R2 × S1 and are in one-to-one correspondence with the theory’s massive vacua. The blocks turn out to have a wealth of surprising properties such as Stokes phenomena and have interesting dual interpretations in analytically continued Chern-Simons theory and open topological strings.

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The paper “On localised hotspots of an urban crime model” by David Lloyd and Hayley O’Farrell has been accepted for publication in Physica D.  In the paper they investigate stationary, spatially localised crime hotspots on the real line and the plane of an urban crime model of Short et al (2008).  Extending the weakly nonlinear analysis of Short et al, they show in one dimension that localised hotspots should bifurcate off the background spatially homogenious state at a Turing instability provided the bifurcation is subcritical.  Using path-following techniques, they continue these hotspots and show that the bifurcating pulses can undergo the process of homoclinic snaking near the singular limit.  We analyse the singular limit to explain the existence of spike solutions and compare the analyical results with the numerical computations.  In two dimensions, we show that localised radial spots should also bifurcate off the spatially homogeneous background state.  Localised planar hexagon fronts and hexagon patches are found and depending on the proximity to the singular limit these solutions either undergo homoclinic snaking or act like “multi-spot” solutions.  Finally, we discuss applications of these localised patterns in the urban crime context and the full agent-based model.  A copy of the final form preprint can be downloaded here.

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The paper “A regularization of the carbon cycle data fusion problem” has been accepted for oral presentation at the 2013 general assembly of the European Geophysical Union.  It will appear in session NP5.1.  The presenter is Sylvain Delahaies and his co-authors are Ian Roulstone and Nancy Nicholls (Reading).  AGU2013 will take place the week of 07 April in Vienna.  The website for AGU2013 can be found here.

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Tom Bridges gave a talk in the Industrial and Applied Mathematics Seminar series at the University of Nottingham on 20th February and a talk in the Applied Mathematics Series at the University of Reading on 26th February.  The title of the talk in both cases was “Reappraisal of two myths in the theory of nonlinear waves“.  The first myth is that the shallow water equations (SWEs) are a model for shallow water hydrodynamics.  It is shown that in fact the shallow water equations can not control the growth of horizontal vorticity and so the equations will in general break down.  Although the SWEs are a perfectly valid mathematical model, they may be invalid when applied to realistic shallow water oceanographic flows.  The second myth is how the KdV equation arises as a model PDE.  The conventional view is that the KdV equation arises as a model when the dispersion relation of the linearization of some system of PDEs has the appropriate form, and the nonlinearity is quadratic.  A new mechanism is presented which shows that the KdV equation always takes a universal form where the coefficients in the KdV equation are completely determined from the modulation properties of the background state — even when the background state is the trivial solution!   One outcome is that “shallow water” is neither necessary nor sufficient for the emergence of the KdV equation.

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The paper “On the massless modes of the AdS3/CFT2 integrable systems” has been accepted for publication in the Journal of High Energy Physics (JHEP).  The 83 page paper is co-authored by Olof Ohlsson Sax (University of Utrecht), Bogdan Steganski Jr (City University London) and Alessandro Torrielli.  In the paper they make a proposal for incorporating massless modes into the spin-chain of the AdS3/CFT2 integrable system.  They do this by considering the alpha –> 0 limit of the alternating delta(2,1;alpha)^2 spin-chain constructed in arXiv:1106.2558.  In the process they encounter integrable spin-chains with non-irreducible representations at some of their sites.  They investigate their properties and construct their R-matrices in terms of Yangians.  A final-form preprint of the paper can be found on the arXiv.

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Gianne Derks visited the University of Keele on Wednesday 20 February to give a talk in the Applied Mathematics Seminar series.   The title of the talk is “Viscosity-induced instability for Euler and averaged Euler equations in a circular domain“.

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