Thu, 01 Oct 2015

17:00 - 18:00
L1

Dancing Vortices

Étienne Ghys
(Ecole Normale Superieure, Lyons)
Abstract
Oxford Mathematics Public Lectures
 
This lecture has now sold out
 
There will be a special public lecture at 5pm on October 1 in the Andrew Wiles Building at Oxford University, during the week of the Clay Mathematics Institute’s annual Research Conference.  The lecture will be given in English by the French Mathematician Étienne Ghys and will be designed for A-level students (and above). After the lecture, Professor Ghys will be presented with the first Clay Award for the Dissemination of Mathematical Knowledge.
 
Abstract 
Nineteenth century observations of the behaviour of smoke rings and fluid vortices inspired an ingenious but misconceived model of the atom, a flawed proposal that nonetheless gave birth to the modern theory of knots. The chain of ideas has now come full circle with recent theoretical and experimental results on the existence of knotted vortices.
 
Clay Award for Dissemination 

The first Clay Award for Dissemination of Mathematical Knowledge has been made to Étienne Ghys in recognition of his own important contributions to mathematical research and for his distinguished work in the promotion of mathematics. 

Étienne Ghys  is a CNRS Directeur de Recherche at ENS, Lyon.  He has published outstanding  work in his own fields of geometry and dynamics,  both under his own name and under the collaborative pseudonym “Henri Paul de Saint Gervais”—contributions recognised by invitations to speak at the International Congress in 1990 and by his elevation to the French Académie des Sciences in 2004.  He has also given invaluable service to the international mathematical community in many contexts, as a member of the program committee for the ICM in Hyderabad, as a member of the Fields Medal committee in 2014, and through service on many other bodies. 

But it  is through his work in the promotion of mathematics in France and elsewhere that he has become a legend.  He has given numerous carefully crafted lectures to audiences ranging from school children to delegates at the International Congress in 2006, when he gave a beautiful and exceptionally clear plenary lecture on Knots and dynamics.  He has enthusiastically embraced modern technology to aid the exposition of deep ideas, for example during his editorship of Images des mathématiques, which he transformed to an online publication in 2009, and which received more than five million visits over his five-year term of office. He himself has written more than 90 articles for Images, as well as a monthly column in Le Monde.  

He created with others the Maison de mathématiques et informatique  in Lyon and co-founded, with Dierk Schleicher, the International summer school of mathematics for young students. His series of films, produced with Aurélien Alvarez and Jos Leys and published as DVDs and online in many languages, has had a huge impact on high school students.  The first, Dimensions, has been downloaded more than a million times.

 

Departmental teaching awards announced

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. 

 

Thu, 03 Dec 2015

16:00 - 17:00
L3

Sharp interface limit in a phase field model of cell motility

Leonid v Berlyand
(PSU)
Abstract

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.

Mon, 29 Jun 2015
15:45
L6

On Unoriented Topological Conformal Field Theories

Ramses Fernandez-Valencia
(Oxford)
Abstract

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.

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