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In September 2013, as Oxford Mathematics moved in to its new building, Marcus Du Sautoy gave four public lectures covering a range of topics from symmetry to prime numbers, music to the mathematical limits of knowledge. All four lectures were broadcast on Japanese television and are now available to watch online.

The Music of the Primes: a talk about the Riemann Hypothesis and primes

Symmetry: a talk based on his second book, 'Finding Moonshine'

The Secret Mathematicians: the connections between maths and the arts

The Irrational, the Chaotic and Incomplete: the mathematical limits of knowledge

All four form part of the new Oxford Podcasts series The Secrets of Mathematics.

The Nomura lecture 2014 will take place at The Mathematical Institute on Thursday 5th June 2014. The speaker is Edward Prescott (Nobel laureate 
in economics 2004).

Title: Time Inconsistency with Application to the Design of a Sustainable Financial System

Abstract: 

The most valuable asset that people in a sovereign state can have is good, sustainable governance.  Setting up a system of good, sustainable governance is not easy.  The big and well-known problem is time inconsistency of optimal policies.  A mechanism that has proven valuable in mitigating the time inconsistency problem is rule by law. The too-big-to-fail problem in banking is the result of the time inconsistency problem.  In this lecture I will argue there is an alternative financial system that is not subject to the too-big-to-fail problem. The alternative arrangement I propose is a pure transaction banking system.  Transaction banks are required to hold 100% interest bearing reserves and can pay tax-free interest on demand deposits.  With this system, there cannot be a bank run as there is no place to run to.  Mutual arrangements would finance all business investment, which is not currently the case.

Sir Michael Atiyah OM, FRS, FRSE is one of the great mathematicians of the last hundred years and to celebrate his 85th birthday a one-day meeting will be held here in Oxford in the Mathematical Institute on 22 April 2014. The meeting will also see the publication by Oxford University Press of a seventh volume of his collected works. Please contact Frances Kirwan (@email) if you would like to attend the meeting.

Timetable and speakers:

 9.30  Nigel Hitchin - Surfaces, geodesics and hyperkahler geometry

10.30 Coffee

11.00 Graeme Segal - Solitons and inverse scattering

 2.30  Sergei Gukov - The Atiyah-Segal-Singer equivariant index theorem for the Hitchin moduli space

 3.30  Tea

 4.30  Robbert Dijkgraaf - Geometry and matrices 

 5.30  Reception

The convergence of the scientific disciplines has gathered pace in recent years and nowhere was this more visible than in the 2014 Oxford Brain Mechanics Workshop held in Oxford on 13 and 14 January 2014. Understanding the brain, its pathology, injury and healing is no longer just a priority for clinicians but is a field where data analysis and mathematical modelling can work with clinical practice to further our understanding of the most complex of human organs.

14 speakers represented a range of disciplines from medical sciences, neuroscience, and biology to engineering, physics and mathematics. Areas of focus included modelling of brain tissue, normal and abnormal brain development and the impact of traumatic brain injury. Over 70 delegates attended the workshop, the second of the series, sharing ideas and beginning the critical process of collaboration.

The workshop was organised by the newly founded International Brain Mechanics and Trauma Lab (IBMTL) with the support of the Oxford Centre Collaborative Applied Mathematics (OCCAM). IBMTL is an international collaboration on projects related to brain mechanics and trauma based in Oxford. This multidisciplinary team is motivated by the need to study brain cell and tissue mechanics and its relation with brain functions, diseases or trauma.

The speakers were as follow:

Prof. Gerhard Holzapfel (Graz University of Technology), Prof. Ellen Kuhl (Stanford University), Dr Peter Stewart (University of Glasgow) and Dr Jeremiah Murphy (Dublin City University) talked about their research on the characterization and mathematical modelling of brain tissue.

Dr Waney Squier (Oxford University Hospitals), Dr David Edwards (Kings College London), Dr Jay Jayamohan (JR Hospital, Oxford) and Dr Nick de Pennington (Oxford University Hospitals) shared their invaluable clinical experiences and research on normal and abnormal human brain development and personalised neurosurgery.

Prof. Lee Goldstein (Boston University), Prof. Anthony Bull (Imperial College London), Prof. Riyi Shi (Purdue University) and Prof. Fernando Maestu (Complutense University of Madrid) presented their traumatic brain injury studies from different perspectives, such as acute injury, chronic sequelae, investigation of CNS injury, and reorganization of functional brain networks in traumatic brain injury.

Dr Stephen Payne (University of Oxford) and Dr Ferath Kherif (Centre Hospitalier Universitaire Vaudois) showed their great efforts on bridging the gap between mathematical models/ new data mining technologies and clinical practice. 

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.