Analysis Seminar
The seminars are held on Thursdays at 16:00 in Room B3.02  Mathematics Institute unless noted otherwise
Term 2 2019/20
Organiser: Lucas Ambrozio, Filip Rindler
09 Jan Alessandro Pigati (ETHZürich) Codimension two minmax minimal submanifolds from PDEs
16 Jan No seminar
23 Jan No seminar
30 Jan Spencer BeckerKahn (Cambridge) Stationary varifolds near multiplicity two planes
06 Feb Lucas Ambrozio (Warwick) Minmax width and volume of Riemannian three dimensional spheres
13 Feb Giacomo del Nin (Warwick) Pattern formation in planar partitions
20 Feb Pieralberto Sicbaldi (Granada) Existence and regularity of FaberKrahn minimizers in a Riemannian manifold
27 Feb Jonas Azzam (Edinburgh) Poincaré inequalities, uniform rectifiability, and Dorronsoro's Theorem
05 Mar Angkana Rüland (MaxPlanck Leipzig) Uniqueness, stability and single measurement recovery for the fractional Calderon problem
11 Mar 2pm Bobby Wilson (Washington) Marstrand's Theorem for uniformly convex norms
12 Mar Pierre Raphaël (Cambridge) On energy super critical blow up for waves and fluids
Term 1 2019/20
Organiser: Filip Rindler, Lucas Ambrozio
3/10/19  Ovidiu Munteanu (Connecticut, visiting UCL) 
Green's function estimates and the Poisson equation
Abstract: The Green's function of the Laplace operator has been widely studied in geometric analysis. Manifolds admitting a positive Green's function are called nonparabolic. By Li and Yau, sharp pointwise decay estimates are known for the Green's function on nonparabolic manifolds that have nonnegative Ricci curvature. The situation is more delicate when curvature is not nonnegative everywhere. While pointwise decay estimates are generally not possible in this case, we have obtained sharp integral decay estimates for the Green's function on manifolds admitting a Poincare inequality and an appropriate (negative) lower bound on Ricci curvature. This has applications to solving the Poisson equation, and to the study of the structure at infinity of such manifolds.

10/10/19  Franz Gmeineder (Bonn) 
Regularity for quasiconvex functionals with linear growth from below 
17/10/19  Diogo Oliveira e Silva (Birmingham) 
Global maximisers for spherical restriction 
24/10/19  Adolfo ArroyoRabasa (Warwick) 
A variational characterization of oscillations and concentrations ocurring along a PDEconstrained sequence 
31/10/19  NO TALK  
7/11/19  David Bourne (HeriotWatt) 
Optimal Lattice Quantizers and Best Approximation in the Wasserstein Metric 
14/11/19  NO TALK  
21/11/19  Konstantinos Koumatos (Sussex) 
On the vectorial Weierstrass problem and some applications
Abstract: In the calculus of variations, the Weierstrass problem consists in finding sufficient conditions for a given map to be a local minimiser in an appropriate topology. The talk presents some recent developments in the vectorial setting, since its resolution by Grabovsky and Mengesha in 2009, including an alternative proof and an extension to nonsmooth domains. Surprisingly, the proof has consequences in the theory of conservation laws with involutions which are discussed.

28/11/19  Stefano Borghini (Uppsala) 
Static vacuum spacetimes with positive cosmological constant 
5/12/19  Jonathan BenArtzi (Cardiff) 
Convergence rates in dynamical systems lacking a spectral gap
Abstract: Our world is neither compact nor periodic. It is therefore natural to consider dynamical systems on unbounded domains, where typically there is no spectral gap. I will present a (simple) method for studying the generators of such systems where a spectral gap assumption is replaced with an estimate of the Density of States (DoS) near zero. There are two main applications:
1) Dissipative systems: when the generator is nonnegative, an estimate of the DoS leads to a socalled "weak Poincaré inequality" (WPI). This in turn leads (in some cases) to an algebraic decay rate for the $L^2$ norm of the solution. For instance, in the case of the Laplacian (generator of the heat equation) the WPI is simply the Nash inequality which leads to the optimal decay rate of $t^{d/4}$.
2) Conservative systems: when the generator is skewadjoint, an estimate of the DoS leads to a uniform ergodic theorem on an appropriate subspace. Examples include the linear Schrödinger equation and incompressible flows in Euclidean space. Based on joint works with Amit Einav (Graz) and Baptiste Morisse (Cardiff). 