List of Abstracts
Nicholas Alikakos (University of Athens)
Title: Hierarchical Structure-Stratification for the Allen-Cahn System
Abstract:
Ioannis Anappolitanos (KIT, Karlsruhe)
Title: Van der Waals forces between atoms and molecules and an application to isomerizations
Abstract: The van der Waals forces are universal attractive forces between atoms and molecules. They play a role in chemistry, biology, material sciences and physics. These forces are of quantum nature and it is long being conjectured and experimentally verified that they have universal behaviour at large separations: they are attractive and decay as the inverse sixthpower of the pairwise distance between the atoms or molecules. We will first explain how to prove this conjecture, under some assumptions, for a system of atoms and then how to modify the proof so that it works for a system of molecules. Time permitting at the end of the talk we will explain an application of the van der Waals forces to isomerizations, namely to chemical reactions where the reactant and the product consist of the same atoms but with different bindings.
The talk is based on 3 works one of which is joint work with Michael Sigal and another of which is a joint work with Mathieu Lewin.
Dimitra Antonopoulou (University of Chester)
Title: Existence and regularity of solution for a stochastic Cahn–Hilliard/Allen–Cahn equation with unbounded noise diffusion
Abstract:
We consider the stochastic Cahn–Hilliard/Allen–Cahn equation with a multiplicative space-time rough noise with unbounded diffusion coefficient. Applying techniques from semigroup theory, we prove local existence and uniqueness in dimensions d = 1, 2, 3. Moreover, when the noise diffusion satisfies a sub-linear growth condition of order bounded by 1/3, which is the inverse of the polynomial order of the nonlinearity used, we prove for d = 1 global existence of solution. Path regularity of stochastic solution, depending on that of the initial condition, is obtained a.s. up to the explosion time. Our results are also valid for the stochastic Cahn–Hilliard equation with unbounded noise diffusion, for which previous results were established only in the framework of a bounded diffusion coefficient. As expected from the theory of parabolic operators in the sense of Petrovskıı, the bi-Laplacian operator seems to be dominant in the combined model.
Joint with Georgia Karali and Annie Millet.
Volker Bach (TU Braunschweig)
Title: The Hartree-Fock-Bogolubov Equations for Boson Systems
Abstract:
The time-dependent Hartree-Fock-Bogoliubov equation for
bosons is derived as a natural dynamical generalization of the
(stationary) Hartree-Fock approximation from quantum chemistry (for
fermions). It is shown that it possesses a natural symplectic
structure reminiscent of a Hamiltonian system. Its conservation laws
are analyzed, and its global well-posedness is established.
Jeremy Faupin (Université Lorraine)
Title: Scattering theory for dissipative quantum systems
Abstract:
In this talk, we will consider an abstract pseudo-hamiltonian given by a dissipative operator of the form H = H_V - i C^*C, where H_V = H_0 + V is self-adjoint and C is a bounded operator. Such operators are frequently used to study scattering theory for dissipative quantum systems. We will recall conditions implying existence of the wave operators associated to H and H_0, and we will see that they are asymptotically complete if and only if H does not have spectral singularities on the real axis. For Schrödinger operators, the spectral singularities correspond to real resonances.
This is joint work with Jürg Fröhlich.
Greg Fournodavlos (University of Cambridge)
Title: Singularity formation in black hole interiors
Abstract:
There is wide expectation in the physics community that black hole solutions to the Einstein equations should contain a terminal singularity in their interior region. However, apart from spherically symmetric models, very little is known. I will begin by reviewing celebrated work of Roger Penrose in the 60's ("singularity theorem", "strong cosmic censorship") that motivated the black hole interior problem. Then I will move on to some classical work in spherical symmetry, including the resolution of the spherically symmetric scalar field model by Christodoulou in the early 90's. Finally, I will present recent developments that go beyond spherical symmetry, for "near Schwarzschild" black hole interiors, in the context of the Einstein equations in vacuum.
Gian Michele Graf (ETH-Zürich)
Title: Disorder and topology. The cases of Floquet and of chiral systems.
Abstract:
We will present a new formulation of bulk and edge indices for
disordered Floquet systems. A byproduct is a space-time duality
stating the equivalence of two settings: two systems may be placed
next to one another in space or operate one after the other in time.
A different type of systems to be addressed are disordered chiral
chains, which may be viewed as Su-Schrieffer-Heeger
models with random hopping. There localization occurs at all but
possibly one energy, which is enough to endow the model with
topological features. Different formulations of the index will be
introduced and related to the Lyapunov spectrum of the chain.
Radu Ignat (Université Paul Sabatier, Toulouse)
Title: On the uniqueness of minimisers of Ginzburg-Landau functionals
Abstract:
We provide necessary and sufficient conditions for the uniqueness of minimisers of the Ginzburg-Landau functional for vector valued maps with a boundary data that is non-negative in a fixed direction. Furthermore, we show that, when minimisers are not unique,
the set of minimisers is generated from any of its elements using appropriate orthogonal transformations. We also prove corresponding results for harmonic maps.
This is a joint work with L. Nguyen (Oxford), V. Slastikov (Bristol) and A. Zarnescu (Bilbao).
Mathieu Lewin (Paris Dauphin)
Title: Gross-Pitaevskii-type Gibbs measures and their derivation from many-body quantum mechanics
Abstract:
In this talk I will define and discuss some probability measures in infinite dimensions, which play an important role in (S)PDE, in Quantum Field Theory and for Bose-Einstein condensates. Those are Gibbs measures associated with the Gross-Pitaevskii and Hartree energies. In dimensions larger than or equal to 2, the measures are concentrated on distribution spaces, and the nonlinear term has to be renormalized. I will then present some results in collaboration with Phan Thanh Nam and Nicolas Rougerie about the derivation of these measures from many-body quantum mechanics in a mean-field type limit.
Research funded by ERC grant MDFT.
Christof Melcher (RWTH Aachen)
Title: Topological Solitons in Chiral Magnets
Abstract:
Michael Israel Sigal (University of Toronto)
Title: On mathematics of chemotaxis
Abstract:
Jan Philip Solovej (University of Copenhagen)
Title: The Bogoloubov variational functional for Bose gases
Abstract:
I will discuss a variational formulation of the famous Bogolubov approximation. I will discuss existence and lack of uniqueness of minimizers as well as Bose-Sinstein condensation in this model. I will then turn to studying the functional in the dilute limit and explain that it gives rather accurate asymptotics for the free energy and the critical temperature.
David Stuart (University of Cambridge)
Title: Relative Entropy Method and Continuum Limit in Elastodynamics
Abstract:
Daniel Ueltschi (University of Warwick)
Title: From condensed matter physics to probability theory
Abstract:
The basic laws governing atoms and electrons are well understood, but it is impossible to make predictions about the behaviour of large systems of condensed matter physics. A popular approach is to introduce simple models and to use notions of statistical mechanics. I will review quantum spin systems and their stochastic representations in terms of random permutations and random loops. I will also describe the universal behaviour that is common to loop models in dimensions 3 and more (“Poisson-Dirichlet”).
Stephanos Venakides (Duke University)
Title: Integrable PDE with small dispersion
Abstract:
