Department of Mathematics

Search

PDE and mathematical physics

×

Modal title

Modal content

Autumn Semester 2018

Date / Time Speaker Title Location
20 September 2018
18:10-19:00 		Anne-Sophie de Suzzoni
Université Paris 13
Event Details

PDE and Mathematical Physics

Title [Video] Weak turbulence
Speaker, Affiliation Anne-Sophie de Suzzoni, Université Paris 13
Date, Time 20 September 2018, 18:10-19:00
Location Y27 H 35/36
Abstract Abstract : Wave turbulence is the study of the evolution of the statistics of random waves. Weak turbulence corresponds to taking an equation, coming from hydrodynamics or quantum mechanics, which is weakly nonlinear (that is we let its nonlinearity go to zero in a certain regime). One aim of this talk is to present the first aspects of the theory of weak turbulence from a mathematical physics point of view, explain which intrinsically nonlinear behavior it describes, its link with resonances and the growth of Sobolev norms. We will then present some rigorous results and perspectives. One aim is to introduce the computational tool of Feynmann diagrams in this context, its relevance and importance in fully developing the mathematical study of weak turbulence. We will discuss a joint work with Nikolay Tzvetkov and an ongoing project with Zaher Hani.,Slides
[Video] Weak turbulenceread_more
Y27 H 35/36
27 September 2018
15:00-16:00 		Alix Deleporte
University of Strasbourg
Event Details

PDE and Mathematical Physics

Title Toeplitz operators and the large spin limit
Speaker, Affiliation Alix Deleporte, University of Strasbourg
Date, Time 27 September 2018, 15:00-16:00
Location Y27 H 46
Abstract The large spin limit is commonly seen as a semiclassical limit. The Berezin-Toeplitz quantization gives a mathematical background to this interpretation. In this talk, I will present this quantization, which is also useful when dealing with problems from Weyl quantization. I will present recent results about the spectrum of Toeplitz operators in the semiclassical limit, in smooth as in analytic regularity, and their applications to the low-temperature properties of frustrated spin systems.
Toeplitz operators and the large spin limitread_more
Y27 H 46
11 October 2018
15:00-16:00 		Enrico Valdinoci
University of Western Australia
Event Details

PDE and Mathematical Physics

Title Chaotic orbits for nonlocal equations and applications to atom dislocation dynamics in crystals
Speaker, Affiliation Enrico Valdinoci, University of Western Australia
Date, Time 11 October 2018, 15:00-16:00
Location Y27 H 46
Abstract In this talk we consider a nonlocal equation driven by a perturbed periodic potential. We construct multibump solutions that connect one integer point to another one in a prescribed way. In particular, heteroclinic, homoclinic and chaotic trajectories are constructed. This result regarding symbolic dynamics in a fractional framework is part of a study of Peierls-Nabarro model for crystal dislocations. The associated evolution equation can be studied in the mesoscopic and macroscopic limits. Namely, the dislocation function has the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. These dislocation points evolve according to the external stress and an interior potential, which can be either repulsive or attractive, depending on the relative orientations of the dislocations. For opposite orientations, collisions occur, after which the system relaxes exponentially fast.
Chaotic orbits for nonlocal equations and applications to atom dislocation dynamics in crystalsread_more
Y27 H 46
25 October 2018
18:10-19:00 		Prof. Dr. Xavier Ros-Oton
Universität Zürich
Event Details

PDE and Mathematical Physics

Title [Video] On the Singular set in the Stefan problem and a conjecture of Schaeffer
Speaker, Affiliation Prof. Dr. Xavier Ros-Oton, Universität Zürich
Date, Time 25 October 2018, 18:10-19:00
Location Y27 H 35/36
Abstract Free boundary problems are those described by PDE's that exhibit a priori unknown (free) interfaces or boundaries. The Stefan problem is the most classical and motivating example in the study of free boundary problems. It describes the evolution of a medium undergoing a phase transition, such as ice passing to water. A milestone in this context is the classical work of Caffarelli (Acta Math. 1977), in which he established for the first time the regularity of free boundaries in the Stefan problem, outside a certain set of singular points. The goal of this talk is to present some new results concerning the size of the singular set in the Stefan problem, proving in particular that, in $\R^3$, for almost every time the free boundary is smooth, with no singularities. This is a joint work with A. Figalli and J. Serra. ,Slides
[Video] On the Singular set in the Stefan problem and a conjecture of Schaefferread_more
Y27 H 35/36
8 November 2018
15:00-16:00 		Anne-Sophie de Suzzoni
Université Paris 13
Event Details

PDE and Mathematical Physics

Title Asymptotics for the Hartree equation
Speaker, Affiliation Anne-Sophie de Suzzoni, Université Paris 13
Date, Time 8 November 2018, 15:00-16:00
Location Y27 H 46
Abstract In this talk, we will present one model (in the mean field limit) for large systems of particles interacting via a potential $w$. This model is a Hartree equation on random fields in $\R^d$ that admits equilibria related to thermodynamical equilibria. We study the asymptotic stability of these equilibria. One issue that arises is the fact that these equilibria are not localised in space, their laws are invariant by translation in space. We prove a scattering result around these equilibria under some assumptions on $w$. The proof is based on a high frequency/low frequency analysis and a reformulation of the problem.
Asymptotics for the Hartree equationread_more
Y27 H 46
15 November 2018
15:00-16:00 		Prof. Dr. Massimiliano Berti
SISSA
Event Details

PDE and Mathematical Physics

Title Dynamics of Water Waves
Speaker, Affiliation Prof. Dr. Massimiliano Berti, SISSA
Date, Time 15 November 2018, 15:00-16:00
Location Y27 H 46
Abstract I shall present recent results about the complex dynamics of the water waves equations of a bi-dimensional fluid under the action of gravity and eventually capillary forces, with space periodic boundary conditions. This is an infinite dimensional Hamiltonian system. We shall discuss both long time existence results as well as bifurcation of small amplitude time quasi-periodic solutions. Major difficulties are the quasi-linear nature of the water waves equations and complex resonance phenomena.
Dynamics of Water Wavesread_more
Y27 H 46
22 November 2018
15:00-16:00 		Prof. Dr. Clement Mouhot
Cambridge University
Event Details

PDE and Mathematical Physics

Title Title T.B.A.
Speaker, Affiliation Prof. Dr. Clement Mouhot, Cambridge University
Date, Time 22 November 2018, 15:00-16:00
Location Y27 H 46
Title T.B.A.
Y27 H 46
13 December 2018
15:00-16:00 		Prof. Dr. Jean-Pierre Marco
Université Pierre et Marie Curie - Paris 6
Event Details

PDE and Mathematical Physics

Title On the integrability of the geodesic flow on infinite dimensional ellipsoids
Speaker, Affiliation Prof. Dr. Jean-Pierre Marco, Université Pierre et Marie Curie - Paris 6
Date, Time 13 December 2018, 15:00-16:00
Location Y27 H 46
Abstract In this talk we will first recall the proof of the integrability of the geodesic flow on finite dimensional ellipsoids, together with the necessary underlying algebraic geometry.This will yield a system of first integrals in involution, which we will prove to extend to the case of the infinite dimensional ellipsoids in $\ell^2(\N)$.
On the integrability of the geodesic flow on infinite dimensional ellipsoidsread_more
Y27 H 46

Note: if you want you can subscribe to the iCal/ics Calender.

Archive: SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 SS 20 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10

JavaScript has been disabled in your browser