Analysis (understood in a wide sense) is a major activity within WIMCS. The research interests within the Cluster include analytic and computational spectral theory; spectral theory of differential operators on domains, manifolds and graphs, including operators arising in mathematical physics and non-self-adjoint problems; function spaces and integral operators; inverse problems; analytic number theory; qualitative theory of elliptic and parabolic second order linear, semi-linear and quasi-linear partial differential equations; applications of semigroup theory to partial differential equations, Markov semi-groups and perturbation theory of generators of semi-groups; vectorial calculus of variations and its applications to material micro-structure models, forward-backward diffusion equations and their applications to image processing, compensated convexity; reaction-diffusion and reaction-diffusion-convection equations and systems, their singular limits, and their applications to population dynamics, travelling waves and mathematical aspects of phase transitions; stochastic partial differential equations; semi-classical methods; systems of fully nonlinear PDEs, studied particularly using convex analysis, variational methods, and concepts from optimal mass transportation; Dirichlet to Neumann maps; functional equations of the Wiener-Hopf type; the theory and applications of the singular equations with fixed point singularities; waves in inhomogeneous lattices; as well as applications in numerical analysis, mathematical bioinformatics, internet security and risk management, archaeology, image recognition, oceanology, plasticity and visco-plasticity, and many others.
Members of the Analysis Cluster enjoy fruitful collaboration with other WIMCS clusters, and also with numerous Universities in the U.K. and in all the continents (except Antarctica). We organize regular Cluster meetings, present series of postgraduate lecture, and have an active visitor programme.
The Cluster day-by-day running is cooordinated by the Steering Committee, which includes
Please contact the co-ordinators for more information on our activities, any suggestions, or, for WIMCS members, to be included in the Cluster mailing list.The cluster poster prepared for the International Review 2010 is here
PEOPLE IN THE ANALYSIS CLUSTER
'@': link to e-mail;
'D': official website at individual's department;
'P': private website
|A Russell Davies||@||D|
|W Des Evans||@||D|
|Karl Michael Schmidt||@||D||P|
Some of the past and future Analysis meetings organized by WIMCS or affiliated with WIMCS Analysis Cluster.
Cardiff University 125th Anniversary Distinguished Visitor Lecture. Wednesday 18 March 2009, Cardiff (Room E/0.15)
Contact Michael Levitin (Cardiff): E-mail
Percy Deift (Courant Institute, New York), Integrable Systems: A Modern View
MOPNET (EPSRC Matrix and Operator Pencils Network) Meeting 0. Monday 30 March - Tuesday 31 March 2009, Cardiff.
Contact Marco Marletta (Cardiff): E-mail
Sixth Wales Workshop on Mathematical Analysis and Modern Applications, Semigroups of operators with application to PDEs. Thursday 23 April 2009, Swansea.
Contact: Vitali Liskevich (Swansea): E-mail
Seventh Wales Workshop on Mathematical Analysis and Modern Applications, Calculus of Variations and nonlinear PDEs. Tuesday, 7 April 2009, Swansea, Civil and Computational Lecture Theatre.
Contact: Kewei Zhang (Swansea), Antonio Orlando and Elaine Crooks (Sansea)Timetable:
- 12:30-1:30pm Lunch
- 1:30-2:20pm Kaushik Bhattacharya (Caltech), TBA
- 2:30-3:20pm Sergio Conti (Bonn), TBA
- 3:30-4:00pm Tea
- 4:00-4.50pm Norman Dancer (Sydney), Stable and finite Morse index solutions of nonlinear elliptic equations
Fifth Wales Workshop on Mathematical Analysis and Modern Applications, Problems in infinite domains with regular ends. Wednesday 11 February 2009, Cardiff.
Contact: Michael Levitin (Cardiff), e-mail Levitin@cardiff.ac.ukTimetable:
- 12:00-13:00 (Room M/2.06) Lunch
- 13:00-13:50 (Room E/0.15) Pavel Exner (Prague), Approximations by Schroedinger operators on networks collapsing to graphs
- Abstract: We revisit the longstanding problem how to understand the coupling in vertices of a quantum graph using an approximation by a family of appropriate “fat graphs”. Recall that if the approximating operators are Neumann Laplacians, the squeezing limit yields only the free (or Kirchhoff) boundary conditions. In this talk we report a recent result coming from a common work with Olaf Post: it will be shown that adding families of suitably scaled potentials one can get spectrally nontrivial vertex couplings, including those with wave functions discontinuous at the vertices. Using recent quantum graph approximation results, we conjecture that in this way one can approximate a large family of vertex couplings.
- 14:00-14:50 (Room E/0.15) Marco Marletta (Cardiff), Dirichlet to Neumann maps and spectral problems for PDEs
- 15:00-15:30 (Room M/2.06) Tea
- 15:30-16:20 (Room E/0.15) Leonid Parnovski (University College London), Spectral properties of periodic pseudo-differential operators for large energy
- Abstract: I will discuss recent results on spectral properties of periodic operators. I will concentrate on Bethe-Sommerfeld conjecture and the asymptotic behaviour of the integrated density of states
- 16:30-17:20 (Room E/0.15) Pierre Duclos (Toulon and Marseilles), On scattering and spectral questions in quantum transport
- Abstract: We shall review questions and results in a model of quantum transport in mesoscopic systems when an electrical bias is introduced adiabatically. We shall discuss existence and computation of a NESS (non equilibrium steady state) as well as the current ﬂowing in the mesoscopic system. We shall present new challenging questions about N-body scattering in open manifold with inﬁnite cylindrical ends as well as quantum evolution when the instantaneous discrete spectrum merges in the continuum. This is a joint work with H. Cornean, C. Gianesello, H. Nenciu et R. Purice. To learn about this topic one may consult the article J. Math. Phys. 49, 102106 (2008) arXiv math-ph/0708.0303, where the linear response approach of these questions is considered.
- 17:30-18:00 (Room E/0.15) Q&A session with Pavel Exner on the work of the European Research Council
Fourth Wales Workshop on Mathematical Analysis and Modern Applications, 30 April 2008, Swansea.Talks:
- Rob Douglas (Aberystwyth), Introduction to Optimal Mass Transfer and its applications
- Alexander Plakhov (WIMCS, Aberystwyth), Optimal mass transportation and problems of optimal aerodynamic resistance
- Boris Khesin (Toronto) A nonholonomic Moser theorem and optimal mass transport
- Geoffrey Burton (Bath), Equimeasurable rearrangements and stability of vortices in the half-plane
Third Wales Workshop on Mathematical Analysis and Modern Applications, Spaces and Operators on Bad Domains in Rn. In honour of Desmond Harris in the year of his 80th birthday. 30 April 2008, Cardiff.Talks:
- W Des Evans (Cardiff), Analysis on domains in Rn with irregular (even fractal) boundaries
- David Edmunds (Cardiff), Operators of Hardy type
- Yuri Netrusov (Bristol), Estimates of s-numbers of Sobolev embeddings in domains
Second Wales Workshop on Mathematical Analysis and Modern Applications, 30 January 2008, Cardiff.Talks:
- W Des Evans (Cardiff), On some fundamental inequalities in Analysis
- Michael Levitin (WIMCS/Cardiff), Old and new estimates of low eigenvalues of the Laplacians
- Ari Laptev (Imperial), On some new function and spectral inequalities
First Wales Workshop on Mathematical Analysis and Modern Applications, 31 October 2007, Swansea.Talks:
- Kewei Zhang (WIMCS/Swansea), Introduction to Calculus of Variations and related issues in PDEs
- John Ball (Oxford), Orientability of director fields for liquid crystals
- Igor Verbitsky (Birmingham), Quasi-linear and fully nonlinear equations of Lane-Emden type
NEWS AND VACANCIES
There are no vacancies at present.