10 October 2011

Speaker: Anne-Maria Ernvall-Hytonen.

Title: On short exponential sums connected with cusp forms.

Abstract: I will briefly tell about the history of exponential sums involving Fourier coefficients of cusp forms, and how they connect to the exponential sums involving values of the divisor function. I will then turn to the short sums, and tell what we know about them, what we believe about them, how they connect to the values of individual coefficients, and what kind of computer data we have.

24 October 2011

Speaker: Vitaly Moroz (Swansea).

Title: Asymptotic properties of ground states of a semilinear elliptic problem with a vanishing parameter.

Abstract: We consider a semilinear elliptic problem on the entire space with a double-well type nonlinearity. When one of the parameters vanishes the ground state of the problem converges after a suitable rescaling to the ground state of a limiting problem, however the form of the limiting equation depends on whether the original problem contains a subcritical, critical or supercritical term. We establish the precise asymptotic rate of the limiting rescaling and derive asymptotic behaviour of the ground states at the origin and near infinity.
This is a joint work with Cyrill Muratov (NJIT, USA).

31 October 2011

Analysis and Applied Mathematics Octoberfest Cardiff 2011.
This event will start with a lunch at 12:00 in Room M/1.04 and will be followed by the following 3 talks, the first of which starts at 14:10. Please note all talkes will take place in M2.06.

13:10-14:00

Speaker: Elaine Crooks (Swansea).

Title: Highly nonlinear large-competition limits of elliptic systems.

Abstract: In this talk, I will discuss the effect of different types of competitive interaction terms on the large-interaction limit of nonlinear elliptic systems modelling the steady states of populations that compete in some region. As the competition rate tends to infinity, non-negative solutions of quite simple-looking systems converge to the positive and negative parts of solutions of a scalar limit problem which may be much more strongly nonlinear than the original system, possibly with quadratic growth in the gradient of the limit function. This is joint work with Norman Dancer.

14:30-15:20

Speaker: Alan Haynes (Bristol).

Title: Separated nets which are bounded displacement from a lattice.

Abstact: A subset Y of a metric space is called a separated net if there are constants r, R>0 such that every ball of radius R intersects Y and every ball of radius r contains at most one point of Y. There is a technique in tiling theory called the `cut and project method' which provides an abundant source of separated nets in Euclidean space. Until recently it was an open problem to determine whether separated nets coming from this method can be deformed in a uniform way onto a lattice. In this talk we will describe these ideas in more detail and explain our proof that almost all separated nets coming from the cut and project method can be translated onto a lattice by moving each point by at most some fixed constant distance. This is joint work with Barak Weiss and Michael Kelly.

15:40-16:30

Speaker: Martin Sieber (Bristol).

Title: Semiclassical approach to discrete symmetries in quantum chaos.

Abstract: We use semiclassical methods to evaluate spectral statistics of quantum systems that are classically chaotic and possess discrete spatial symmetries. The energy spectra of these systems fall into subspectra that are associated to irreducible representations of the corresponding symmetry group. We show that for (spinless) time reversal invariant systems the spectral two-point correlation function for subspectra associated to real and complex representations, respectively, coincide with predictions from the Gaussian Orthogonal Ensemble (GOE) and the Gaussian Unitary Ensemble (GUE) of Random Matrix Theory. For systems without time reversal invariance all subspectra show GUE statistics.

7 November 2011

Speaker: Federica Dragoni (Cardiff).

Title: X-convexity and applications.

Abstract:We introduce a new notion of convexity, namely X -convexity, which applies to any given family of vector fields and in particular to the sub-Riemannian case. We then show a PDE-characterization for X-convex functions and we investigate some properties of these functions. (Joint work with Martino Bardi).

9 November 2011 at 15:10 in Room M/2.06

Speaker: Marco Marletta (Cardiff).

Title: Weak stability for inverse Sturm-Liouville problems with finite data.

Abstract:The talk will be based on a paper I published in 2005 with Rudi Weikard.

It shows that if one knows, up to error \epsilon, the first N
Dirichlet-Dirichlet and Dirichlet-Neumann eigenvalues for a Sturm-Liouville
problem in Liouville normal form with square summable potential then
the potential is determined up to an error

const.(\epsilon \log(N) + N^{-1/2})

in a W^{-1,\infty} norm.

The method of proof is by transformators, which I will introduce and
discuss, and generalized eigenfunction expansions.

14 November 2011

Speaker: Ralf Rueckriemen (Cardiff).

Title: Isospectrality on quantum graphs.

Abstract: I will discuss the two main methods to build isospectral quantum graphs. The first method is inherited from combinatioral graphs, one uses Seidel switching to build isospectral combinatorial graphs, and then applies investigates under what circumstances these give rise to isospectral quantum graphs. The second method is called Sunada's method. It was originally designed for manifolds but there are versions for quantum graphs.

15 November 2011 from 10:00am in Room M/1.25

WIMCS/Leverhulme Postdoctoral Fellowships

10:00-10:35

Speaker: Shane Cooper (University of Bath).

10:35-11:10

Speaker: Veronique Fischer (Imperial College London).

11:10-11:45

Speaker: Michael Strauss (Heriot-Watt University).

21 November 2011

Speaker: Gabor Kiss (Exeter).

Title: Currency exchange rate fluctuations by delay differential equations.

Abstract: In many applications the rate of change of state variables depends on their states at prior times. When these processes are assumed to be deterministic, they are modelled by delay differential equations. In the simplest cases only one, time invariant time lag is considered. However, equations with multiple delays offer richer dynamics, thus they are of mathematical interest and potential models of real-world problems with complex oscillations. We present results on the coexistence of periodic solutions to an equation with two point delays; a novel rigorous computational tool which allows us deriving valuable existence results for these infinite dimensional dynamical systems is also described. Furthermore, we report on the existence of pullback attractors to equations with multiple time-varying delays. A model for exchange-rate fluctuations is considered as a motivating example.

28 November 2011

Speaker: Nicolas Dirr (Cardiff).

Title: Minimizers of random functionals.

Abstract: We consider a class of functionals on Sobolev spaces which consist of a part penalizing spatial oscillations of the function (i.e. the $L62$-norm of the gradient or a nonlocal version thereof) a double-well potential which prefers the function to be close to either $+1$ or $-1,$ and a random field, which, while neutral in average, prefers locally the $+1$ or $-1$ state. The competition of these three terms leads to very different behaviour of the minimizers, depending on the space dimension and choice of parameters.

30 November 2011

Speaker: Sergey Naboko (St.Petersburg State University).

Title: On the boundary version of the Analytic Fredholm Theorem and its applications.

Abstract: The classical Analytic Fredholm Theorem determines the invertibility of the analytic operator -valued function in an open domain provided it point wise differs from Identity operator by a compact one.The talk deals with the problem of its invertibility almost everywhere on the boundary important in many problems of perturbation theory including the scattering theory. A counterexample proving the result sharpness to be presented.

5 December 2011

Speaker: Sergei Fedotov.

Title: Fractional reaction-transport equations.

Abstract: I will talk about how to incorporate the nonlinear terms into non-Markovian master equations corresponding to random walks with non-exponential waiting time distributions. I will show how to derive nonlinear fractional partial differential equations for subdiffusive transport. I apply these equations to the problem of front propagation in the reaction-transport systems.

6 February 2012 at 15:10 in Room M/2.06

Speaker: Yaroslav Kurylev.

Title: Mathematical Aspects of Invisibility.

Abstract: We consider so me recent results regarding the mathematical theory of invisiblity, in particular, the problem os convergence of the systems described by the "realistic", i.e, isotropic, non-singular conductivities to the idealised ones. We also discuss some new physical phenomena due to cloacking, e.g. cloaked sensors, etc.

This is a joint work with A. Greenleaf, M.Lassas and G.Uhlmann.

20 February 2012 at 15:10 in Room M/2.06

Speaker: Sanju Velani (York).

Title: Diophantine approximation, fractal sets and lacunary sequences.

Abstract: The metric theory of Diophantine approximation on fractal sets is developed in which the denominators of the rational approximates are restricted to lacunary sequences. The case of the standard middle third Cantor set and the sequence {3^n : n \in N} is the starting point of our investigation. Our metric results for this simple setup answers a problem raised by Mahler. As with all ‘good’ problems – its solution opens up a can of worms.

27 February 2012 at 15:10 in Room M/2.06

Speaker: Laura Caravenna (Oxford).

Title: TBC.

Abstract: TBC.

5 March 2012

Spectral Analysis Day. More information to follow...

19 March 2012 at 15:10 in Room M/2.06

Speaker: Ralf Rueckriemen (Cardiff).

Title: TBC.

Abstract: TBC.

26 March 2012 at 15:10 in Room M/2.06

Speaker: Leonid Parnovski.

Title: TBC.

Abstract: TBC.

23 April 2012 at 15:10 in Room M/2.06

Speaker: Jonathan Bennett (Birmingham).

Title: TBC.

Abstract: TBC.

2 May 2012 at 15:10 in Room M/2.06

Speaker: Johannes Zimmer (Bath).

Title: TBC.

Abstract: TBC.