Robyn Smith, a third year MMath student, has had her abstract selected for presentation at the Tomorrow’s Mathematician Today 2013 Conference.  The conference will be held on Saturday 16 February at the University of Greenwich, and is sponsored by IMA and GCHQ.  Robyn’s talk will be based on her summer 2012 research project on “Game Theory Models of Bone Cancer” which was funded by an EPSRC Vacation Bursary and supervised by Anne Skeldon.  An abstract of her talk is as follows.  Multiple Myeloma is a type of blood cancer which develops in the bone.  The presence of Multiple Myeloma cells can disrupt the balance of other cells in the bone marrow environment.  Evolutionary game theory is used to model the new frequencies of cells and determine how to resolve the balance to a healthy level.  Using evolutionary game theory, the interactions between cells can be analysed to identify Evolutionary Stable States (ESS).  This describes how the cancer will progress in a patient.  Further analysis reveals how changing entries in  the payoff matrix alters the ESS and in particular how to create ESS which are free of cancer cells.

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Martin Wolf will be giving a talk at the week-long conference on “Symmetry and Geometry of Branes in String/M Theory” to be held at Durham University during 28th January to 1st February.  Martin’s talk is on “Non-abelian self-dual tensor field theories from twistor space“.  The conference website is here.

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Martin Wolf’s paper, co-authored with Christian Saemann (Heriot-Watt University), has appeared in the latest issue of the Journal of Mathematical Physics.  The paper is “On twistors and conformal field theories from six dimensions“.  The paper discusses chiral zero-rest-mass field equations on six-dimensional space-time from a twistorial point of view.  Specifically, the paper presents a detailed cohomological analysis, develops both Penrose and Penrose–Ward transforms, and analyses the corresponding contour integral formulæ.  The paper also gives twistor space action principles.  Then the twistor space of six-dimensional space-time is reduced to obtain twistor formulations of various theories in lower dimensions. Besides well-known twistor spaces, a novel twistor space is found amongst these reductions, which turns out to be suitable for a twistorial description of self-dual strings. For these reduced twistor spaces, the Penrose and Penrose–Ward transforms are explained as well as contour integral formulæ.  The published version can be found here.

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Mark Roberts, Anne Skeldon, Cesare Tronci and Claudia Wulff attended the workshop on “Symmetry, bifurcation and order parameters” which was held the week of 7 January at the Newton Institute Cambridge.  This workshop is part of the 6 month programme on “The mathematics of liquid crystals“.  The workshop was organised by David Chillingworth and Peter Palffy-Muhoray and further details can be found here.

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Third year undergraduate James Goodwin has been selected to be one of the speakers in the Tomorrow’s Mathematician Today 2013 Conference.  The conference will be held on Saturday 16 February at the University of Greenwich, and is sponsored by IMA and GCHQ.  James’ talk will be based on his summer 2012 project on “Lie Algebras and Quantum Mechanics” sponsored by the Nuffield Foundation and supervised by Allessandro Torrielli.  The accepted abstract of the talk follows: the talk will look at the connection between areas of Lie theory and quantum mechanics.  Assuming only a familiarity with matrix manipulation, the concept of a “Lie Algebra” will be introduced and used to compare classical simple harmonic with the quantum harmonic oscillator.  The talk will then explore the canonical form of Pauli matrices and how they are applied to the quantum-mechanical concept of spin.  The talk will finish with a brief non-technical description of how Lie algebras occur in a problem at the frontier of theoretical physics – the Yangian algebra associated with the anti-de-Sitter/conformal field theory correspondence.

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Ian Morris’ paper on “Extremal sequences of polynomial complexity“, joint with Nikita Sidorov (University of Manchester) and Kevin Hare (University of Waterloo, Canada), has recently been accepted for publication in the Mathematical Proceedings of the Cambridge Philosophical Society.  A summary of the paper follows.  The joint spectral radius of a finite set of square matrices is defined to be the largest possible exponential growth rate of long products of matrices drawn from that set. In the influential 1995 article “The finiteness conjecture for the generalized spectral radius of a set of matrices“, Jeffrey Lagarias and Yang Wang conjectured that this maximum possible rate of growth can always be realized by multiplying together a periodic sequence of matrices.  This conjecture was shown to be false in 2002 by Thierry Bousch and Jean Mairesse, who gave an example in which the maximum growth rate is only achieved by sequences of matrices which have at least linear subword complexity.  In this article the authors investigate how strongly Lagarias and Wang’s conjecture can fail to be true by constructing an example in which the maximum growth rate can only be achieved by sequences of matrices which have at least polynomial subword complexity.  The final form preprint is available on the arXiv.

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Cesare Tronci & Claudia Wulff are long-term visitors at the Newton Institute Programme on “The Mathematics of Liquid Crystals“.  Cesare is visiting for 8 weeks during the period 7 January to 28 February.  Claudia is visiting for 4 weeks during the period 7 January to 1 February.  Details of the programme can be found at the Newton website.

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Last year, Aston published a paper called “Is radioactive decay really exponential?” (Euro Phys Lett 97 52001).  The paper questioned the almost universally accepted belief that radioactive decay is always exponential.  He considered various arguments that suggest that slowly decaying isotopes may decay non-exponentially, which is hard to verify experimentally due to the long timescales involved.  This work was reviewed in a brief article in the CERN Courier.  The article invited both experimental and theoretical input from the scientific community.  The Cern Courier, established in 1959, reports news and events related to CERN’s high-energy physics community.

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James Grant has been appointed to a Readership in Mathematics at the University of Surrey, starting 2nd January 2012.  James received his PhD from the University of Cambridge in 1993, supervised by Stephen Hawking.  Since then he has held postdoctoral positions at the University of Pittsburgh, University of Newcastle, University of Hull,  and the Universita degle Studi dell’Aquila.  Since 2005 he has been at the University of Vienna.  In 2009 he was awarded a Habilitation for a thesis on Integrable Systems and Differential Geometry by the University of Vienna.  His research is in the areas of differential geometry, mathematical physics and the analysis of nonlinear partial differential equations.  His most recent published paper, with Jan-Hendrik Treude, is on Volume comparison for hypersurfaces in Lorentzian manifolds and singularity theorems, which has recently appeared in the Annals of Global Analysis and Geometry.  A link can be found here.

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Bin Cheng has been appointed to a Lectureship in Mathematics at the University of Surrey starting 2nd January 2012.  Bin received his PhD from the University of Maryland in 2007, supervised by Eitan Tadmor.  He was a Postdoctoral Assistant Professor at the University of Michigan from 2007-2010, and a Visiting Assistant Professor at Arizona State University from 2010-2012.  Bin works in the area of analysis of nonlinear partial differential equations, most recently working on the Euler equations on a rotating sphere.  In October he was co-organizer of a Special Session on Mathematical Fluid Dynamics and its Application in Geosciences, at the American Mathematical Society Section Meeting held at the University of Arizona, 27-28 October.  His Arizona State Unversity website can be seen here .

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