The David Crighton Medal

Reports

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THE DAVID CRIGHTON MEDAL Report The 2015 IMA-LMS David Crighton Medal of communication networks has had direct was awarded to Professor Frank Kelly, CBE, application to the design of telephone FRS, Hon FIMA, at The Royal Society on 12 networks and internet protocols. The im- May 2016. portance and impact of his work more The audience of IMA members, LMS broadly is reflected in the large number of members and invited guests was welcomed citations his papers receive, together with by the President of the IMA, Professor the award of international prizes. He is Chris Linton, CMath FIMA, who reminded the Head of a Cambridge college, and has the audience that the David Crighton chaired groups working to improve chil- Medal was instituted in 2002 in memory dren’s experience of mathematics. He has of Professor David Crighton, who was been Chief Scientific Adviser to the Gov- President of the IMA and President-desig- ernment (Department for Transport) and nate of the LMS. chaired the Council for the Mathemati- Professor Simon Tavaré, FRS FIMA, LMS cal Sciences at an important time for the President, then introduced Frank Kelly, mathematics community. He was elected reading the citation below and introduc- a Fellow of the Royal Society in 1989 and ing Frank’s talk with the observation that awarded a CBE in 2013. Frank has always had a way of making Professor Frank Kelly began his engaging 22 very difficult things seem very simple. The lecture by remembering how well-loved citation reads: David Crighton was at Cambridge and Frank Kelly is awarded the David Crighton showing us some photos at www.damtp. Medal of the London Mathematical Society cam.ac.uk/about/dgc/. and the Institute of Mathematics and its The lecture, Mathematics and Financial Applications for services both to mathe- Markets, centred around a simple and an- matics and to the mathematical community. alytically tractable model of a limit order Kelly’s work on the fundamental properties book that Frank developed with Elena

Simon Tavaré presents Frank Kelly Simon Tavaré, Frank Kelly and Chris the award to Frank Kelly Linton (l to r) [email protected] No. 460 July 2016

Yudovina (http://arxiv.org/abs/1504.00579). advanced mathematics (not less) as is often Frank suggested that this simple model suggested after the 2008 financial crash. could be used to gain insight into trading After the lecture Chris Linton thanked the strategies and allow regulators (and speaker for an excellent talk that demon- society) to decide which trading behaviours strated how a simple mathematical model they would like to encourage. Frank also can have real world applications. noted that many mathematics graduates Rebecca Waters are traders, but few are regulators and IMA Editorial Officer suggested that the market needs more Mathematics Today

CECIL KING TRAVEL SCHOLARSHIP Report I used the Cecil King Travel Scholarship to connection ceofficients matrices provide travel to visit Sheehan Olver at the Uni- an explicit, computable formula for the versity of Sydney for three months from spectral measure. January to April 2016. We worked on We also investigated the infinite di- some problems in computational spectral mensional QL algorithm, which allowed theory and related problems in orthogo- us to formulate a method of transform- nal polynomials. ing these Jacobi operators to a canonical 23 The first outcome of my research was form and implement a functional calculus. that the so-called connection coefficient We were able to store these highly struc- matrix, which is the change of basis matrix tured infinite dimensional matrices in between two families of orthogonal finite memory and perform the opera- polynomials, is a useful new tool for the tions without losing that information: it is spectral theory of the Jacobi operators. I an early example of truly infinite dimen- proved that for Jacobi operators that are sional numerical linear algebra. a finite rank perturbation of Toeplitz, the Alex Townsend (MIT) also visited Sheehan for three weeks in February. We discovered that the connection coefficient matrix for Jacobi polynomials with different param- eters can be decomposed using Hadamard products of Toeplitz and Hankel matrices, leading to a new class of fast polynomial transforms. I am very grateful to the London Mathematical Society and the Cecil King Founda- tion for not only giving me an opportunity to develop as a researcher, but also to © Marcus Webb escape the British winter.

Marcus Webb Marcus Webb University of Cambridge