UoA 20: Pure Mathematics

Pure mathematics at UCL has maintained an extremely active research environment during the last 6 years. One of the most obvious indications of this is the capacity of the department to recruit and retain young researchers of the highest calibre: Csornyei who holds a Wolfson Research Merit Award, Talbot who holds a Royal Society 5-year Fellowship and Yafaev who was recently awarded a Philip Leverhulme Prize. Research achievements have been recognised during the period by, among other things, the election of Preiss to FRS, 3 invited (morning) lectures at British Mathematics Colloquia, an invited lecture at the inaugural conference of the Heilbronn Institute, an Austrian medal of science awarded to Larman, a Whitehead Prize awarded to Csornyei, a Leverhulme Research Fellowship awarded to Parnovski, an invited lecture at the ICM (2006) by Barany and a Leverhulme Senior Research Fellowship awarded to Ball.

UCL is the British node of the EU Marie Curie Research Training Network entitled Phenomena in High Dimensions. This network encompasses 13 institutions throughout Europe and roughly 120 mathematicians. Its aim is to promote the training of young research mathematicians in the fields of high-dimensional geometry, asymptotic combinatorics and statistical physics. Within the UK, researchers in these fields at Cambridge, Edinburgh, Lancaster and Oxford are also attached to the network. From 2004 to 2008, it will fund around 50 secondments of graduate students to different nodes within the network and around 25 (longer) secondments of postdoctoral researchers. The network supports 3-4 meetings per year, including the main annual meeting. The two annual meetings to date have been incorporated into highly successful semester programmes at the Schroedinger Institute (Vienna) and the Institut Henri Poincare (Paris).

In the last couple of years UCL has provided a dramatic injection of new investment into the department enabling the recruitment of 3 new professors, 1 reader and 2 lecturers in pure mathematics and over the RAE period the pure research group has increased in size by 4. The new appointments, Kim, Sobolev, Halburd, Petridis, Vassiliev and Sidorova were selected from very strong fields of applicants.

Throughout the period, the department was an internationally recognised centre for geometric measure theory, high-dimensional geometry, combinatorics and discrete geometry. The researchers in these areas, Ball, Barany, Csornyei, Laczkovich, Larman, McMullen, Preiss, Scott, Sokal, Talbot and Wisewell, all belong to the RTN network and frequently work together.

The appointments of Vassiliev and Sobolev in an area close to that of Parnovski have created an exceptionally strong group in the spectral theory of PDEs. The development of this area was listed in RAE2001 as a priority for the department: this priority has been firmly achieved. A new appointee, Sidorova, who works in probability theory and PDEs, will provide a bridge between the two analysis groups.

At the start of the period, the algebra/number theory group comprised Hill, Johnson and Yafaev and has recently been strengthened by the appointment of Kim who startled the number theory community in the last few years with his introduction of new topological methods into Diophantine geometry. Two other new appointees, Halburd and Petridis, who work in analytic number theory and the spectral theory of automorphic forms, will also provide a link between the analysis and number theory groups.

Download full text of the RA5a statement for Pure Mathematics (pdf 76Kb)

Staff names below link to submitted publications:

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