Six Oxford Mathematicians are among the 2015 London Mathematical Society prizewinners.
A Polya Prize was awarded to Professor Boris Zilber for his visionary contributions to model theory and its applications.
A Naylor Prize and Lectureship in Applied Mathematics was awarded to Professor Jon Chapman (pictured) for his outstanding contributions to modelling and methods development in applied mathematics.
Whitehead Prizes were awarded to the following:
Congratulations to Oxford Mathematicians Dmitry Belyaev, Ian Hewitt, Derek Moulton, Christoph Reisinger, Zubin Siganporia (pictured), Robert Style, Nick Trefethen and Sarah Waters who have all won departmental teaching awards for the year.
OxTALENT is an annual competition and a ceremony designed to recognise and award colleagues and students from across the University for creative use of digital technologies in teaching, learning and outreach.
We study the motion of a eukaryotic cell on a substrate and investigate the dependence of this motion on key physical parameters such as strength of protrusion by actin filaments and adhesion. This motion is modeled by a system of two PDEs consisting of the Allen-Cahn equation for the scalar phase field function coupled with a vectorial parabolic equation for the orientation of the actin filament network. The two key properties of this system are (i) presence of gradients in the coupling terms and (ii) mass (volume) preservation constraints. We pass to the sharp interface limit to derive the equation of the motion of the cell boundary, which is mean curvature motion perturbed by a novel nonlinear term. We establish the existence of two distinct regimes of the physical parameters. In the subcritical regime, the well-posedness of the problem is proved (M. Mizuhara et al., 2015). Our main focus is the supercritical regime where we established surprising features of the motion of the interface such as discontinuities of velocities and hysteresis in the 1D model, and instability of the circular shape and rise of asymmetry in the 2D model. Because of properties (i)-(ii), classical comparison principle techniques do not apply to this system. Furthermore, the system can not be written in a form of gradient flow, which is why Γ-convergence techniques also can not be used. This is joint work with V. Rybalko and M. Potomkin.
We give a classification of open Klein topological conformal field theories in terms of Calabi-Yau $A_\infty$-categories endowed with an involution. Given an open Klein topological conformal field theory, there is a universal open-closed extension whose closed part is the involutive version of the Hochschild chains associated to the open part.
