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Spring Semester 2019

Date / Time Speaker Title Location
24 January 2019
15:00-16:00 		Leonardo Tolomeo
University of Edinburgh
Event Details

PDE and Mathematical Physics

Title [Video] Ergodicity for stochastic dispersive equations
Speaker, Affiliation Leonardo Tolomeo, University of Edinburgh
Date, Time 24 January 2019, 15:00-16:00
Location Y27 H 46
Abstract Abstract: In this talk, we study the long time behaviour of some stochastic partial differential equations (SPDEs). After introducing the notions of ergodicity, unique ergodicity and convergence to equilibrium, we will discuss how these have been proven for a very large class of parabolic SPDEs. We will then shift our attention to dispersive SPDEs, where the general strategy for the parabolic case fails. We will describe this failure for wave equation on the 1-dimensional torus and present a result that settles unique ergodicity even in this case. ,PDF
[Video] Ergodicity for stochastic dispersive equationsread_more
Y27 H 46
28 February 2019
14:00-15:00 		Prof. Dr. Sergey Dobrokhotov
Ishlinsky Institute for Problems in Mechanics of Russian Academy of Sciences
Event Details

PDE and Mathematical Physics

Title Feynman-Maslov calculus of noncommuting operators and application to adiabatic and homogenization problems
Speaker, Affiliation Prof. Dr. Sergey Dobrokhotov, Ishlinsky Institute for Problems in Mechanics of Russian Academy of Sciences
Date, Time 28 February 2019, 14:00-15:00
Location Y27 H 12
Abstract We discuss some ideas and elementary useful formulas from the Feynman-Maslov calculus of noncommuting operators (pseudodifferential operators with a small parameter) and their applications to adiabatic problems. As example we consider the problems from physics of low-dimensional structures (quantum waveguides) and homogenization problems for partial differential equations with rapidly oscillating coefficients.
Feynman-Maslov calculus of noncommuting operators and application to adiabatic and homogenization problemsread_more
Y27 H 12
21 March 2019
17:10-18:00 		Dr. David Lannes
Université de Bordeaux
Event Details

PDE and Mathematical Physics

Title [Video] The shoreline problem for the Green-Naghdi equations
Speaker, Affiliation Dr. David Lannes, Université de Bordeaux
Date, Time 21 March 2019, 17:10-18:00
Location Y27 H 12
Abstract Abstract: The Green-Naghdi equations are a nonlinear dispersive perturbation of the nonlinear shallow water equations, more precise by one order of approximation. These equations are commonly used for the simulation of coastal flows, and in particular in regions where the water depth vanishes (the shoreline). The local well-posedness of the Green-Naghdi equations (and their justification as an asymptotic model for the water waves equations) has been extensively studied, but always under the assumption that the water depth is bounded from below by a positive constant. In this talk we will see how to remove this assumption. The problem then becomes a free-boundary problem since the position of the shoreline is unknown and driven by the solution itself. For the (hyperbolic) nonlinear shallow water equation, this problem is very related to the vacuum problem for a compressible gas. The Green-Naghdi equation include additional nonlinear, dispersive and topography terms with a complex degenerate structure at the boundary. In particular, the degeneracy of the topography terms makes the problem loose its quasilinear structure and become fully nonlinear. Dispersive smoothing also degenerates and its behavior at the boundary can be described by an ODE with regular singularity. These issues require the development of new tools, some of which of independent interest such as the study of the mixed initial boundary value problem for dispersive perturbations of characteristic hyperbolic systems, elliptic regularization with respect to conormal derivatives, or general Hardy-type inequalities. This is joint work with G. Métivier. Ref: D. Lannes and G. Métivier. The shoreline problem for the one-dimensional shallow water and Green- Naghdi equations. J. Ec. polytech. Math., 5:455-518, 2018.,Slides
[Video] The shoreline problem for the Green-Naghdi equationsread_more
Y27 H 12
28 March 2019
14:00-15:00 		Dr. Raphael Winter
University of Bonn
Event Details

PDE and Mathematical Physics

Title Convergence of the weak coupling limit to the Landau equation for the truncated BBGKY hierarchy
Speaker, Affiliation Dr. Raphael Winter, University of Bonn
Date, Time 28 March 2019, 14:00-15:00
Location Y27 H 12
Abstract We show that in macroscopic times of order one, the solutions to the truncated BBGKY hierarchy (to second order) converge in the weak coupling limit to the solution of the nonlinear spatially homogeneous Landau equation. The truncated problem describes the formal leading order behavior of the underlying particle dynamics, and can be reformulated as a non- Markovian hyperbolic equation which converges to the Markovian evolution described by the parabolic Landau equation. The analysis in this paper is motivated by Bogolyubov's derivation of the kinetic equation by means of a multiple time scale analysis of the BBGKY hierarchy.
Convergence of the weak coupling limit to the Landau equation for the truncated BBGKY hierarchyread_more
Y27 H 12
4 April 2019
14:00-15:00 		Dr. Mihalis Mourgoglou
Department of Mathematics, University of the Basque Country, EHU
Event Details

PDE and Mathematical Physics

Title Uniform rectifiability, harmonic measure and Carleson measure estimates for bounded harmonic functions
Speaker, Affiliation Dr. Mihalis Mourgoglou, Department of Mathematics, University of the Basque Country, EHU
Date, Time 4 April 2019, 14:00-15:00
Location Y27 H 12
Abstract In this talk we will give an overview of the recent developments on free boundary problems for harmonic measure. In particular, we will discuss the connection between uniform rectifiability of the boundary of the domain with scale invariant PDE estimates for bounded harmonic functions as well as certain quantitative absolute continuity assumptions for harmonic measure with respect to the Hausdorff measure on the boundary.
Uniform rectifiability, harmonic measure and Carleson measure estimates for bounded harmonic functionsread_more
Y27 H 12
18 April 2019
18:10-19:10 		Dr. Jérémie Szeftel
CNRS and Sorbonne Université
Event Details

PDE and Mathematical Physics

Title [Video] The nonlinear stability of Schwarzschild
Speaker, Affiliation Dr. Jérémie Szeftel, CNRS and Sorbonne Université
Date, Time 18 April 2019, 18:10-19:10
Location Y27 H 35/36
Abstract Abstract: I will discuss a joint work with Sergiu Klainerman on the stability of Schwarzschild as a solution to the Einstein vacuum equations with initial data subject to a certain symmetry class.,PDF
[Video] The nonlinear stability of Schwarzschildread_more
Y27 H 35/36
2 May 2019
14:00-15:00 		Dr. Amit Einav
Karl-Franzens-Universität Graz
Event Details

PDE and Mathematical Physics

Title Weak Poincaré inequalities and the absence spectral gaps
Speaker, Affiliation Dr. Amit Einav, Karl-Franzens-Universität Graz
Date, Time 2 May 2019, 14:00-15:00
Location Y27 H 12
Weak Poincaré inequalities and the absence spectral gaps
Y27 H 12
16 May 2019
14:00-15:00 		Laurent Lafleche
Paris Dauphine
Event Details

PDE and Mathematical Physics

Title Semiclassical limit from Hartree to Vlasov equation
Speaker, Affiliation Laurent Lafleche, Paris Dauphine
Date, Time 16 May 2019, 14:00-15:00
Location Y27 H 12
Abstract The Vlasov equation describes the evolution of a system of particles in interaction at a mesoscopic scale. Its counterpart in quantum mechanics is the Hartree equation and it can be proved that it converges in some sense to the Vlasov equation when the Planck constant \hbar becomes negligible. In this talk, I will present how this convergence can be quantitatively measured by introducing the Wigner transform and semiclassical versions of the Wasserstein-Monge-Kantorovitch distance and the kinetic Lebesgue norms. One of the key step to reach this result is the propagation in time of semiclassical moments and weighted Schatten norms of the solution, which implies the boundedness of the spatial density of particles. This can be proved by using the formal analogies between the Vlasov equation and the density operator formulation of quantum mechanics.
Semiclassical limit from Hartree to Vlasov equationread_more
Y27 H 12
23 May 2019
14:00-15:00 		Dr. Bruno Vergara
Universität Zürich
Event Details

PDE and Mathematical Physics

Title Carleman estimates and boundary observability for waves with critically singular potentials
Speaker, Affiliation Dr. Bruno Vergara, Universität Zürich
Date, Time 23 May 2019, 14:00-15:00
Location Y27 H 12
Abstract In this talk I will present a novel family of Carleman inequalities on cylindrical spacetime domains featuring a potential that is critically singular, diverging as the inverse square of the distance to the boundary. These estimates, which we prove using geometric multiplier arguments that generalize the classical Morawetz inequality, are sharp in the sense that they capture both the natural boundary conditions and the natural $H^1$-energy. Quantitative uniqueness properties such as the boundary observability for the associated wave equations and parabolic analogues of the estimates will be discussed as well. This is based on joint work with A. Enciso and A. Shao.
Carleman estimates and boundary observability for waves with critically singular potentialsread_more
Y27 H 12

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