Thu, 22 Oct 2015

16:00 - 17:00
L3

Information processing in feedforward neuronal networks

Alex Cayco Gajic
(UCL)
Abstract

Feedforward layers are integral step in processing and transmitting sensory information across different regions the brain. Yet experiments reveal the difficulty of stable propagation through layers without causing neurons to synchronize their activity. We study the limits of stable propagation in a discrete feedforward model of binary neurons. By analyzing the spectral properties of a mean-field Markov chain model, we show when such information transmission persists. Addition of inhibitory neurons and synaptic noise increases the robustness of asynchronous rate transmission. We close with an example of feedforward processing in the input layer to cerebellum. 

Thu, 15 Oct 2015

16:00 - 17:00
L3

Localized Patterns & Spatial Heterogeneitie

Arjen Doelman
(Leiden University)
Abstract

We consider the impact of spatial heterogeneities on the dynamics of 
localized patterns in systems of partial differential equations (in one 
spatial dimension). We will mostly focus on the most simple possible 
heterogeneity: a small jump-like defect that appears in models in which 
some parameters change in value as the spatial variable x crosses 
through a critical value -- which can be due to natural inhomogeneities, 
as is typically the case in ecological models, or can be imposed on the 
model for engineering purposes, as in Josephson junctions. Even such a 
small, simplified heterogeneity may have a crucial impact on the 
dynamics of the PDE. We will especially consider the effect of the 
heterogeneity on the existence of defect solutions, which boils down to 
finding heteroclinic (or homoclinic) orbits in an n-dimensional 
dynamical system in `time' x, for which the vector field for x > 0 
differs slightly from that for x < 0 (under the assumption that there is 
such an orbit in the homogeneous problem). Both the dimension of the 
problem and the nature of the linearized system near the limit points 
have a remarkably rich impact on the defect solutions. We complement the 
general approach by considering two explicit examples: a heterogeneous 
extended Fisher–Kolmogorov equation (n = 4) and a heterogeneous 
generalized FitzHugh–Nagumo system (n = 6).

Wed, 22 Jul 2015
12:00
L5

Einstein Metrics, Harmonic Forms, and Symplectic Manifolds.

Claude LeBrun
(Stonybrook)
Abstract
Given a smooth compact 4-manifold M  which admits Einstein metrics, is its moduli space of Einstein metrics connected?  While the corresponding question in higher dimensions typically has a negative answer, there are interesting 4-manifolds M for which the answer is known to be affirmative. One important class of 4-manifolds for which we do not know the answer, however,  consists of the underlying 4-manifolds of the del Pezzo surfaces. In this lecture, I will explain a  result which provides interesting partial information concerning this case. 

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:

How rare is the Bullet Cluster (in a ΛCDM universe)?
Kraljic, D Sarkar, S Journal of Cosmology and Astroparticle Physics volume 1504 issue 4 050-050 (28 Apr 2015)
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, Dimensionshas been downloaded more than a million times.

 

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. 

 

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