# Archive of Previous Activities: Seminars

Maxwell Institute for Mathematical Sciences Analysis Seminar
 Mon 24 May 2010University of Edinburgh JCMB 5215 2.00pm Christos Papadimitropoulos The Fourier restriction phenomenon in thin sets Mon 29 Mar 2010University of Edinburgh JCMB 6301 2.00pm Gabriel Koch (Oxford) An alternative approach to regularity for the Navier-Stokes equations in critical spaces Abstract In an important recent paper, L. Escauriaza, G. Seregin and V. Sverak [ESS] show that solutions to the Navier-Stokes equations (NSE) which remain bounded in $L3(R3)$ (a critical" space) cannot become singular in finite time. This, coupled with a decay result for global solutions by I. Gallgher, D. Iftimie and F. Planchon, is the same type of result which has been proved recently for critical" hyperbolic/dispersive equations by C. Kenig and F. Merle. Their method (which relies on profile decompositions" for bounded sequences) is quite general in nature and thus it is natural to ask whether it can be applied in the NSE setting to give an alternative proof of [ESS]. In collaboration with C. Kenig this has been achieved in the special case of $\dot H^{{1/2}}$ due to the profile decomposition of I. Gallagher in that setting. A similar decomposition has now been established in $L3$ as well, and we therefore expect to be able to generalize our result soon to the more general setting of [ESS]. Thu 18 Mar 2010Heriot-Watt University EM G.44 4.15pm Thomas Sorensen (Imperial College) Regularity properties of Coulombic wavefunctions and their one-electron densities Abstract We review recent results on the regularity and structure of wavefunctions psi of the non-relativistic Schroedinger operator describing atoms and molecules (that is, with Coulomb interactions). We also discuss the regularity of the associated one-electron densities rho. In particular, we characterize the structure of psi around 'two-particle coalescence points'. The method of proof of the latter extends to the study of the structure of the solutions to the multiconfiguration equations, and their densities, at the positions of the nuclei. Mon 15 Mar 2010University of Edinburgh JCMB 5215 2.00pm Nick Michalowski/Longo (Edinburgh) Local Existence Theory for Ultra-hyperbolic Quasilinear Schrodinger Equations Thu 11 Mar 2010Heriot-Watt University EM G.44 4.15pm Hillel Raz (Cardiff University) Local Operators and Locality Bounds in the Anharmonic Lattice Abstract. Local operators are defined as operators which act on local finite sets and outside of that set act as the identity.  In this talk we seek to answer the following question, what happens to local operators under a specific map that corresponds to the time evolution in quantum mechanics.  That is, we seek to find whether or not such operators remain local and if so to what extent.  We do this by comparing the evolved local operator with another local operator that is not evolved and bounding a relation between the two of them.  The result is known as a locality bound, and bears the name of the two who first discovered it - a Lieb-Robinson bound.  We provide such a bound in a few specific settings that come from physics, in particular in the anharmonic lattice. Mon 08 Mar 2010University of Edinburgh JCMB 5215 2.00pm Juan Antonio Barcelo (Madrid) Limiting absortion principle for the Lame equation Thu 25 Feb 2010Heriot-Watt University EM G.44 3.30pm Jens Wirth (Imperial College) Energy and dispersive estimates for hyperbolic systems Abstract. We consider hyperbolic t-dependent pseudo-different systems and present some results on energy and dispersive estimates for their solutions based on a diagonalisation procedure applied to their full symbol. Examples include differential hyperbolic systems as well as hyperbolic differential equations of higher order. David Dos Santos Ferreira (Universite Paris XIII) On the linearized local Calderon problem Thu 18 Feb 2010Heriot-Watt University EM G.44 4.15pm Marko Lindner (TU Chemnitz) Spectra of Jacobi operators: Analysis and approximation Abstract. We look at bounded linear operators on vector-valued $\ell^p$ spaces and study their spectrum (in particular the essential spectrum) and pseudospectra. Our operators are given by infinite matrices with finitely many diagonals. For the case of tridiagonal matrices, we moreover give upper bounds on spectrum and pseudospectrum of the infinite matrix A in terms of pseudospectra of certain submatrices of A. The latter sets approximate the (pseudo-)spectrum of A as $n$ goes to infinity. Mon 15 Feb 2010University of Edinburgh JCMB 5215 2.00pm Jim Wright (Edinburgh) Some elementary number theory revisited from a harmonic analyst's perspective Thu 11 Feb - Sat 13 Feb 2010 Heriot-Watt University all day CANPDE Crash-course in Analysis and Nonlinear PDEs Yvan Martel (Universite de Versailles-Saint-Quentin-en-Yvelines) Francesco Maggi (Universita di Firenze) Thu 28 Jan 2010Heriot-Watt University EM G.44 4.15pm Michael Ruzhansky (Imperial College) Pseudo-differential operators and symmetries Abstract. In this talk we will describe an approach to pseudo-differential operators on Lie groups and homogeneous spaces in terms of their representation theory. This allows one to recapture global symbols of operators and their main properties. The talk will be based on the recent monograph: M. Ruzhansky and V. Turunen, Pseudo-differential operators and symmetries, Birkhauser, Basel, 2010. Mon 18 Jan 2010University of Edinburgh 5215 JCMB 2.00pm Martin Dindos (Edinburgh) The BMO solvability of the elliptic boundary value problem and the A-infinity condition Thu 19 Nov 2009Heriot-Watt University EM 1.70 2.15pm Nicholas Young (Leeds University) Boundary interpolation problems in a half plane Abstract. A classical problem of function theory is to construct (when possible) an analytic function f in the upper half plane Im z > 0 such that Re f(z) is non-negative for all z and such that f satisfies some interpolation conditions at points in the closed upper half plane. I will describe an elementary method for the solution of such problems. Thu 12 Nov 2009University of Edinburgh 4310 JCMB 3.00pm Olga Maleva (Birmingham) Differentiability of Lipschitz functions inside thin sets Tue 10 Nov 2009University of Edinburgh 4310 JCMB 2.00pm Betsy Stovall (UCLA) Quasi-extremals for certain generalized Radon transforms Thu 05 Nov 2009Heriot-Watt University EM 1.70 2.15pm David Rule (Heriot-Watt University) Weighted norm inequalities for pseudodifferential operators defined by amplitudes Mon 2 Nov 2009University of Edinburgh 5215 JCMB 2.00pm Arghir Zarnescu (Oxford) Mathematical problems of the Q-tensor theory Abstract The complexity of nematic liquid crystals is described, in Landau-de Gennes theory, through functions defined on two or three-dimensional domains and taking values into the set of Q-tensors, that is three-by-tree symmetric traceless matrices. The main mathematical challenges are caused by the necessity to finely manipulate high dimensional objects. This large dimensionality of the domain and target space allows for specific features inaccessible in lower dimensions (for instance one needs at least a 2D domain to have a real analytic matrix-valued function with discontinuous eigenvectors). Also, in 2D domains, in the so-called ''constrained theory'', one can express lifting questions in terms of familiar complex analysis problems, but in 3D one needs to construct the appropriate analogue of the complex analytic language in order to effectively deal with the lifting problem, and this is yet to be done. I will present some natural physical questions and recent advances in their mathematical treatment, advances that involve a non-standard combination of diverse tools from analysis, Riemannian geometry, regularity theory and qualitative properties of elliptic and parabolic systems Wed 21 Oct 2009 ICMS 14 India Street 10:00 am PDE Mini-Symposium Thu 15 Oct - Fri 16 Oct 2009 Heriot-Watt University all day CANPDE Crash-course in Analysis and Nonlinear PDEs Laszlo Szekelyhidi (Bonn) Mon 12 Oct 2009University of Edinburgh 5215 JCMB 2.00pm Stefan Valdimarsson (Iceland) Geometric Brascamp--Lieb gives the optimal best constant Abstract We will review the appearances of geometric data in Brascamp--Lieb inequalities. Then we will discuss their role in furnishing the optimal best constant for the Brascamp--Lieb inequalities. Mon 4 Oct 2009University of Edinburgh 5215 JCMB 2.00pm Axel Grunrock (Bonn) Bilinear space-time estimates for linearized kp-type equations with semiperiodic and periodic data Mon 28 Sep 2009University of Edinburgh 5215 JCMB 2.00pm Aram Karakhanyan (University of Edinburgh) On derivation of Euler-Lagrange equations for incompressible energy minimizers