For a logarithmic utility function we extend our rezult with Xu and Zhou for case of the geometrical Brownian motion with drift term which depends of the some hidden parameter.
Anthony Lock will speak on "A Column Model of Moist Convection".
I will speak about the CBP (canonical base property) for types of finite SU-rank. This property first appears in a paper by Pillay and Ziegler, who show that it holds for types of finite rank in differentially closed fields of characteristic 0, as well as in existentially closed difference fields. It is unknown whether this property holds for all finite rank types in supersimple theories. I will first recall the definition of a canonical base, and give some natural examples. I will then talk about a reduction of the problem (which allows one to extend the Pillay-Ziegler result to existentially closed fields of any characteristic), and finally derive some consequences of the CBP, in particular the UCBP, thus answering a question of Moosa and Pillay. If time permits, I will show an application of these results to difference
fields.
An overview of the experiments of Steinbergs group, Theory-and-models and comparison of the applicability of recent reduced models.
Self adjusted meshes have important benefits approximating PDEs with solutions that exhibit nontrivial characteristics. When appropriately chosen, they lead to efficient, accurate and robust algorithms. Error control is also important, since appropriate analysis can provide guarantees on how accurate the approximate solution is through a posteriori estimates. Error control may lead to appropriate adaptive algorithms by identifying areas of large errors and adjusting the mesh accordingly. Error control and associated adaptive algorithms for important equations in Mathematical Physics is an open problem.
In this talk we consider the main structure of an algorithm which permits mesh redistribution with time and the nontrivial characteristics associated with it. We present improved algorithms and we discuss successful approaches towards error control for model problems (linear and nonlinear) of parabolic or hyperbolic type.
A -polarised K3 surface admits an embedding into weighted projective space defined by its polarisation. Let X be a family of such surfaces, then one can construct a projective model W of X such that the map from X to W realises this embedding on the general fibre. This talk considers what happens to W when we allow the fibres of the family X to degenerate.
The semisimplicity problem is the long-standing conjecture that the group algebra $KG$ of a $p'$-group $G$ over a field $K$ of characteristic $p\geqslant 0$ has zero Jacobson radical. We will discuss recent advances in connection with this problem.
We will discuss a connection between small cancellation conditions and isoperimetric inequalities. Additionally we shall look at a useful construction connecting small cancellation complexes and cube complexes.
I will talk about joint work with Dimca, respectively Behrend and Bryan, in which we refine the numerical DT-Behrend invariants of Hilbert schemes of threefolds by using vanishing cycle motives (a la Kontsevich-Soibelman) or mixed Hodge modules, leading to deformed MacMahon formulae.
I will talk about joint work with Dimca, respectively Behrend and Bryan, in which we refine the numerical DT-Behrend invariants of Hilbert schemes of threefolds by using vanishing cycle motives (a la Kontsevich-Soibelman) or mixed Hodge modules, leading to deformed MacMahon formulae.
Two classes of solutions of the Einstein equations with symmetry which
are frequently studied are the Bianchi and Gowdy models. The aim of this
talk is to explain certain relations between these two classes of
spacetimes which can provide insights into the dynamics of both. In
particular it is explained that the special case of the Gowdy models known as circular loop spacetimes are Bianchi models in disguise. Generalizations of Gowdy spacetimes which can be thought of as inhomogeneous perturbations of some of the Bianchi models are introduced.
Results concerning their dynamics are presented.
We study the homogenization and singular perturbation of the
wave equation in a periodic media for long times of the order
of the inverse of the period. We consider inital data that are
Bloch wave packets, i.e., that are the product of a fast
oscillating Bloch wave and of a smooth envelope function.
We prove that the solution is approximately equal to two waves
propagating in opposite directions at a high group velocity with
envelope functions which obey a Schr\"{o}dinger type equation.
Our analysis extends the usual WKB approximation by adding a
dispersive, or diffractive, effect due to the non uniformity
of the group velocity which yields the dispersion tensor of
the homogenized Schr\"{o}dinger equation. This is a joint
work with M. Palombaro and J. Rauch.