Past

Much of group theory is concerned with whether one property entails another. When such a question is answered in the negative it is often via a pathological example. We will examine the Rips construction, an important tool for producing such pathologies, and touch upon a recent refinement of the construction and some applications. In the course of this we will introduce and consider the profinite topology on a group, various separability conditions, and decidability questions in groups.

I'll explain how the `Auslander philosophy' from finite dimensional algebras gives new methods to tackle problems in higher-dimensional birational geometry. The geometry tells us what we want to be true in the algebra and conversely the algebra gives us methods of establishing derived equivalences (and other phenomenon) in geometry. Algebraically two of the main consequences are a version of AR duality that covers non-isolated singularities and also a theory of mutation which applies to quivers that have both loops and two-cycles.

In this talk I will present the rigorous construction of

singular solutions for two kinetic models, namely, the Uehling-Uhlenbeck

equation (also known as the quantum Boltzmann equation), and a class of

homogeneous coagulation equations. The solutions obtained behave as

power laws in some regions of the space of variables characterizing the

particles. These solutions can be interpreted as describing particle

fluxes towards or some regions from this space of variables.

The construction of the solutions is made by means of a perturbative

argument with respect to the linear problem. A key point in this

construction is the analysis of the fundamental solution of a linearized

problem that can be made by means of Wiener-Hopf transformation methods.

Condition supercritical percolation so that the origin is enclosed by a dual circuit whose interior traps an area of n^2.

The Wulff problem concerns the shape of the circuit. We study the circuit's fluctuation. A well-known measure of this fluctuation is maximum local roughness (MLR), which is the greatest distance from a point on the circuit to the boundary of circuit's convex hull. Another is maximum facet length (MFL), the length of the longest line segment of which this convex hull is comprised.

In a forthcoming article, I will prove that

for various models including supercritical percolation, under the conditioned measure,

MLR = \Theta(n^{1/3}\log n)^{2/3}) and MFL = \Theta(n^{2/3}(log n)^{1/3}).

An important tool is a result establishing the profusion of regeneration sites in the circuit boundary. The talk will focus on deriving the main results with this tool

Dislocation channel-veins and Persist Slip Band (PSB) structures are characteristic configurations in material science. To find out the formation of these structures, the law of motion of a single dislocation should be first examined. Analogous to the local expansion in electromagnetism, the self induced stress is obtained. Then combining the empirical observations, we give a smooth mobility law of a single dislocation. The stability analysis is carried our asymptotically based on the methodology in superconducting vortices. Then numerical results are presented to validate linear stability analysis. Finally, based on the evidence given by the linear stability analysis, numerical experiments on the non-linear evolution are carried out.

An overview of the early history of the soliton (1960-1970) and equipartition in nonlinear 1D lattices : From Fermi-Pasta-Ulam to Korteweg de Vries, to Nonlinear Schrodinger*…., and recent developments .

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.

We construct a market of bonds with jumps driven by a general marked point

process as well as by an Rn-valued Wiener process, in which there exists at least one equivalent

martingale measure Q0. In this market we consider the mean-variance hedging of a contingent

claim H 2 L2(FT0) based on the self-financing portfolios on the given maturities T1, · · · , Tn

with T0 T. We introduce the concept of variance-optimal martingale

(VOM) and describe the VOM by a backward semimartingale equation (BSE). We derive an

explicit solution of the optimal strategy and the optimal cost of the mean-variance hedging by

the solutions of two BSEs.

The setting of this problem is a bit unrealistic as we restrict the available bonds to those

with a a pregiven finite number of maturities. So we extend the model to a bond market with

jumps and a continuum of maturities and strategies which are Radon measure valued processes.

To describe the market we consider the cylindrical and normalized martingales introduced by

Mikulevicius et al.. In this market we the consider the exp-utility problem and derive some

results on dynamic indifference valuation.

The talk bases on recent common work with Dewen Xiong.

Traditional Faraday waves appear in a layer of liquid that is shaken vertically. These patterns can take the form of horizontal stripes, close-packed hexagons, or even squares or quasiperiodic patterns. Faraday waves are commonly observed as fine stripes on the surface of wine in a wineglass that is ringing like a bell when periodically forced.

Motivated by recent experiments on Faraday waves in Bose-Einstein condensates we investigate both analytically and numerically the dynamics of cigar-shaped Bose-condensed gases subject to periodic modulation of the strength of the transverse confinement's trap.

We offer a fully analytical explanation of the observed parametric resonance yielding the pattern periodicity versus the driving frequency. These results, corroborated by numerical simulations, match extremely well with the experimental observations.

I shall describe joint work with Gritsenko and Hulek in which we study the moduli spaces of polarised holomorphic symplectic manifolds via their periods. There are strong similarities with moduli spaces of K3 surfaces, but also some important differences, notably that global Torelli fails. I shall explain (conjecturally) why and show how the techniques used to obtain general type results for K3 moduli can be modified to give similar, and quite strong, results in this case. Mainly I shall concentrate on the case of deformations of Hilbert schemes of K3 surfaces.

During the last two years, sparsity has become a key concept in various areas

of applied mathematics, computer science, and electrical engineering. Sparsity

methodologies explore the fundamental fact that many types of data/signals can

be represented by only a few non-vanishing coefficients when choosing a suitable

basis or, more generally, a frame. If signals possess such a sparse representation,

they can in general be recovered from few measurements using $\ell_1$ minimization

techniques.

One application of this novel methodology is the geometric separation of data,

which is composed of two (or more) geometrically distinct constituents -- for

instance, pointlike and curvelike structures in astronomical imaging of galaxies.

Although it seems impossible to extract those components -- as there are two

unknowns for every datum -- suggestive empirical results using sparsity

considerations have already been obtained.

In this talk we will first give an introduction into the concept of sparse

representations and sparse recovery. Then we will develop a very general

theoretical approach to the problem of geometric separation based on these

methodologies by introducing novel ideas such as geometric clustering of

coefficients. Finally, we will apply our results to the situation of separation

of pointlike and curvelike structures in astronomical imaging of galaxies,

where a deliberately overcomplete representation made of wavelets (suited

to pointlike structures) and curvelets/shearlets (suited to curvelike

structures) will be chosen. The decomposition principle is to minimize the

$\ell_1$ norm of the frame coefficients. Our theoretical results, which

are based on microlocal analysis considerations, show that at all sufficiently

fine scales, nearly-perfect separation is indeed achieved.

This is joint work with David Donoho (Stanford University).

We give a three dimensional generalization of the classical McKay correspondence construction by Gonzales-Sprinberg and Verdier. This boils down to computing for the Bridgeland-King-Reid derived category equivalence the images of twists of the point sheaf at the origin of C^3 by irreducible representations of G. For abelian G the answer turns out to be closely linked to a piece of toric combinatorics known as Reid's recipe.