The 2015 Oxford Brain Mechanics Workshop 19 and 20 January, 2015 in St Hugh’s College, Oxford

Everybody is welcome to attend but (free) registration is required.

The event will include speakers from both CMU and Oxford working on Brain Mechanics and Trauma, as well as some chosen international members from the IBMTL* (www.brainmech.ox.ac.uk).

As well as focusing on various aspects of brain mechanics research, the 2015 Oxford Brain Mechanics Workshop will include the UK launch of the Carnegie Mellon University (CMU) – University of Oxford ‘Brain Alliance’. We are delighted that Dr Subra Suresh, President of CMU will launch the workshop, introduced by Oxford Vice-Chancellor Prof. Andrew Hamilton.

The aim of the workshop is to foster new collaborative partnerships and facilitate the dissemination of ideas from researchers in different fields related to the study of brain mechanics, including pathology, injury and healing. The IBMTL is delighted to be a global partner in CMU’s ‘BrainHub’ initiative and further extend the truly interdisciplinary, collaborative network of IBMTL and its associated researchers in Medical Sciences, Neuroscience, Biology, Engineering, Physics and Mathematics.

• Speakers:
• Professor Andrew Hamilton, University of Oxford, UK
• Dr Subra Suresh, Carnegie Mellon University, USA
• Mr Nick de Pennington, University of Oxford, UK
• Professor Michel Destrade, National University of Ireland, Galway
• Dr Kristian Franze, University of Cambridge, UK
• Professor Alain Goriely, University of Oxford, UK
• Professor Gerhard Holzapfel, Graz University of Technology, Austria
• Professor Jimmy Hsia, University of Illinois
• Mr Jayaratnam Jayamohan, University of Oxford, UK
• Professor Antoine Jerusalem, University of Oxford, UK
• Professor Ellen Kuhl, Stanford University, USA
• Professor Philip R LeDuc, Carnegie Mellon University, USA
• Professor Riyi Shi, Purdue University, USA

The workshop is generously supported by the Oxford Centre for Collaborative Applied Mathematics (OCCAM), which is led by IBMTL Co-Director, Prof Alain Goriely.

we discuss various conjectures about the absolute Galois group G_Q  of the field Q of rational numbers and to what extent it encodes the elementary theory of Q.

Both sides of the geometric Langlands correspondence have natural Hecke
symmetries. I will explain an identification between the Hecke
symmetries on both sides via the geometric Satake equivalence. On the
abelian level it relates the topology of a variety associated to a group
and the representation category of its Langlands dual group.
 

Since its genesis in 1915, General Relativity has proven to be one of the most successful physical theories ever invented. Providing a description of the large scale structure of the universe it continues to be in agreement with all experimental tests to high accuracy. By merging Classical Mechanics and Electrodynamics to a consistent geometrical theory of space-time it has become one of the two pillars of modern theoretical physics alongside Quantum Mechanics. This talk aims to give an introduction to the ideas and concepts of General Relativity. After briefly reviewing Classical (Newtonian) Mechanics and experiments in contradiction with it the framework and axioms of General Relativity will be introduced. This will be followed by a survey on major implications of the (new) geometrical description of gravity. Finally an outlook on physics beyond General Relativity will be provided. 

Given a subset E of R^n with empty interior, what is the maximum regularity exponent s for which there exist non-zero distributions in the Bessel potential Sobolev space H^s_p(R^n) that are supported entirely inside E? This question has arisen many times in my recent investigations into boundary integral equation formulations of linear wave scattering by fractal screens, and it is closely related to other fundamental questions concerning Sobolev spaces defined on ``rough'' (i.e. non-Lipschitz) domains. Roughly speaking, one expects that the ``fatter'' the set, the higher the maximum regularity that can be supported. For sets of zero Lebesgue measure one can show, using results on certain set capacities from classical potential theory, that the maximum regularity (if it exists) is negative, and is (almost) characterised by the fractal (Hausdorff) dimension of E. For sets with positive measure the maximum regularity (if it exists) is non-negative,but appears more difficult to characterise in terms of geometrical properties of E.  I will present some partial results in this direction, which have recently been obtained by studying the asymptotic behaviour of the Fourier transform of the characteristic functions of certain fat Cantor sets.