News

Xunyu Zhou was recently elected to be a member of the Council of the Bachelier Finance Society.

Oxford Mathematics Professor Peter Keevash has proved the Existence Conjecture for combinatorial designs, answering a question of Steiner from 1853. 

A Steiner Triple System on a set X is a collection T of 3-element subsets of X such that every pair of elements of X is contained in exactly one of the triples in T. An example considered by Plücker in 1835 is the affine plane of order three, which consists of 12 triples on a set of 9 points. Plücker observed that a necessary condition for the existence of a Steiner Triple System on a set with n elements is that n be congruent to 1 or 3 mod 6. In 1846, Kirkman showed that this necessary condition is also sufficient.

 In 1853, Steiner posed the natural generalisation of the question: given integers q and r, for which n is it possible to choose a collection Q of q-element subsets of an n-element set X such that any r elements of X are contained in exactly one of the sets in Q? There are some natural necessary divisibility conditions generalising the necessary conditions for Steiner Triple Systems. The Existence Conjecture states that for all but finitely many n these divisibility conditions are also sufficient for the existence of general Steiner systems (and more generally designs).

In his paper Peter proves the Existence Conjecture, and more generally, shows that the natural divisibility conditions are sufficient for clique decompositions of simplicial complexes that satisfy a certain pseudorandomness condition.

In October 2013, as the new Mathematical Institute opened, Roger Penrose gave a lecture at the Royal Institution talking about forbidden crystal symmetry in mathematics and architecture and its part in the Penrose tiling which adorns the entrance to the new building. Roger also took questions and answers about his work from the audience.

In October 2013 eminent mathematicians presented the latest thinking about some of the Millennium Problems as part of the Clay Mathematics Research Institute’s Annual Conference held here in the Andrew Wiles Building in Oxford. 

Peter Constantin (Princeton) addressed the Navier-Stokes Equations, Lance Fortnow (Georgia Institute of Technology) the P versus NP Problem, and Fernando Rodriguez Villegas (Austin) the Birch—Swinnerton–Dyer Conjecture.

Other contributions were talks by Edward Witten (Institute for Advanced Study, Princeton) on the Jones Polynomial of a Knot, Richard Thomas (Imperial College) on the work of Clay Research Awardee Rahul Pandharipande and Ingrid Daubechies (Duke) on Animation, Teeth and Skeletons. This last talk formed the link between the Clay Research Conference and the Opening Conference for the Andrew Wiles Building.

As part of its 'Architecture That Shook Oxford' series Oxford Today, profiles the new Mathematical Institute, the Andrew Wiles Building. Dr William Whyte, Fellow of St John's College discusses both the building itself and what it says about the Oxford in the 21st Century.

http://www.oxfordtoday.ox.ac.uk/culture/videos-podcasts-galleries/architecture-shook-oxford-3

Congratulations to Frances Kirwan, FRS, who has been honoured in the 2014 New Year Honours for services to mathematics. Frances, who specialises in algebraic and symplectic geometry, has been a Professor in Oxford since 1996, is a former President of the London Mathematical Society and is Chair of the United Kingdom Mathematics Trust.

Watch Dr Richard Earl from Oxford Mathematics talk about prime numbers as part of the Christmas Science Lectures. Richard not only explains the intrinsic importance of prime numbers, but expands on their role in our everyday lives, notably their critical part in internet security.

Sir Roger Penrose has a long-standing interest in and connection with M C Escher, the Dutch graphic artist best known for his mathematically inspired woodcuts and lithographs. Roger talks about a relationship that dates back nearly sixty years and also explains why art has been a consistent part of both his family life and his mathematics.

Johannes Ruf will deliver the Bruti-Liberati Lecture at the Quantitative Methods in Finance 2013 Conference (17-20 December)

More information on the Conference can be found here http://www.qfrc.uts.edu.au/qmf/

Describing how he came to work in mathematical biology and his passion for the subject, Kit's interview can be heard this Thursday, 05 December, at 8pm on Radio Cardiff 98.7FM & www.radiocardiff.org and will then be available online as a podcast from pythagoras' trousers.