Past

TBA

Synthetic Aperture Radars (SARs) produce high resolution images over large areas at high data rates. An aircraft flying at 100m/s can easily image an area at a rate of 1square kilometre per second at a resolution of 0.3x0.3m, i.e. 10Mpixels/sec with a dynamic range of 60-80dB (10-13bits). Unlike optical images, the SAR image is also coherent and this coherence can be used to detect changes in the terrain from one image to another, for example to detect the distortions in the ground surface which precede volcanic eruptions.

It is clearly very desirable to be able to compress these images before they are relayed from one place to another, most particularly down to the ground from the aircraft in which they are gathered.

Conventional image compression techniques superficially work well with SAR images, for example JPEG 2000 was created for the compression of traditional photographic images and optimised on that basis. However there is conventional wisdom that SAR data is generally much less correlated in nature and therefore unlikely to achieve the same compression ratios using the same coding schemes unless significant information is lost.

Features which typically need to be preserved in SAR images are:

o texture to identify different types of terrain

o boundaries between different types of terrain

o anomalies, such as military vehicles in the middle of a field, which may be of tactical importance and

o the fine details of the pixels on a military target so that it might be recognised.

The talk will describe how Synthetic Aperture Radar images are formed and the features of them which make the requirements for compression algorithms different from electro-optical images and the properties of wavelets which may make them appropriate for addressing this problem. It will also discuss what is currently known about the compression of radar images in general.

tba

We shall explain how to give substance to an old dream of Tits, to invent exotic new zeta functions, and discover the skeleton of algebraic varieties (toric manifolds and tropial geometry).

This talk will introduce L1-regularized optimization problems that arise in image processing, and numerical methods for their solution. In particular, we will focus on methods of the split-Bregman type, which very efficiently solve large scale problems without regularization or time stepping. Applications include image

denoising, segmentation, non-local filters, and compressed sensing.

TBA

Descent theory is the art of gluing local data together to global data. Beside of being an invaluable tool for the working geometer, the descent philosophy has changed our perception of space and topology. In this talk I will introduce the audience to the basic results of scheme and descent theory and explain how those can be applied to concrete examples.

Standard quantum logic, as intitiated by Birkhoff and von Neumann, suffers from severe problems which relate quite directly to interpretational issues in the foundations of quantum theory. In this talk, I will present some aspects of the so-called topos approach to quantum theory, as initiated by Isham and Butterfield, which aims at a mathematical reformulation of quantum theory and provides a new, well-behaved form of quantum logic that is based upon the internal logic of a certain (pre)sheaf topos.

TBA

We shall explain how to give substance to an old dream of Tits, to invent exotic new zeta functions, and discover the skeleton of algebraic varieties (toric manifolds and tropical geometry).

We shall explain how to give substance to an old dream of Tits, to invent exotic new zeta functions, and discover the skeleton of algebraic varieties (toric manifolds and tropical geometry).

The Green-Griffiths conjecture from 1979 says that every projective algebraic variety $X$ of general type contains a certain proper algebraic subvariety $Y$ such that all nonconstant entire holomorphic curves in $X$ must lie inside $Y$. In this talk we explain that for projective hypersurfaces of degree $d>dim(X)^6$ this is the consequence of a positivity conjecture in global singularity theory.

A graph is $\chi$-bounded with a function $f$ is for all induced subgraph H of G, we have $\chi(H) \le f(\omega(H))$.  Here, $\chi(H)$ denotes the chromatic number of $H$, and $\omega(H)$ the size of a largest clique in $H$. We will survey several results saying that excluding various kinds of induced subgraphs implies $\chi$-boundedness. More precisely, let $L$ be a set of graphs. If a $C$ is the class of all graphs that do not any induced subgraph isomorphic to a member of $L$, is it true that there is a function $f$ that $\chi$-bounds all graphs from $C$? For some lists $L$, the answer is yes, for others, it is no.  

A decomposition theorems is a theorem saying that all graphs from a given class are either "basic" (very simple), or can be partitioned into parts with interesting relationship. We will discuss whether proving decomposition theorems is an efficient method to prove $\chi$-boundedness. 

The main aim is to incorporate the nonlinear term into non-Markovian Master equations for a continuous time random walk (CTRW) with non-exponential waiting time distributions. We derive new nonlinear evolution equations for the mesoscopic density of reacting particles corresponding to CTRW with arbitrary jump and waiting time distributions. We apply these equations to the problem of front propagation in the reaction-transport systems of KPP-type.

We find an explicit expression for the speed of a propagating front in the case of subdiffusive transport.