ENS de Lyon meets SISSA Lyon, France December 5-6, 2017

Schedule
• Tuesday, December 5
 8:50am - 9:00am Opening by the directors: Thierry Dauxois (ENS Physics), Alice Guionnet (UMPA), Stefano Ruffo (SISSA) 9:00am - 9:40am Denis Serre 9:40am - 9:50am Andrea Romanino 9:50am - 10:20am Stefano Baroni 10:20am - 11:00am Sergio Ciliberto 11:00am - 11:30am Coffee break 11:30am - 12:10am Gianluigi Rozza 12:10pm - 12:50pm Nathalie Aubrun 1:00pm - 2:30pm Lunch 2:30pm - 3:10pm Giovanni Bussi 3:10pm - 3:50pm Patrice Abry 3:50pm - 4:20pm Coffee break 4:20pm - 5:00pm Guido De Philippis 5:00pm - 5:40pm Vincent Pilloni

• Wednesday, December 6
 9:00am - 9:40am Mokhtar Adda-Bedia 9:40am - 10:20am Marco Bertola 10:20am - 11:00am Alice Guionnet 11:00am - 11:30am Coffee break 11:30am - 12:10am Pasquale Calabrese 12:10pm - 12:50pm Cédric Vaillant 1:00pm - 2:30pm Lunch 2:30pm - 3:10pm Henning Samtleben 3:10pm - 3:50pm Étienne Ghys 3:50pm - 4:20pm Coffee break 4:20pm - 4:30pm Sandro Sorella 4:30pm - 5:00pm Michele Fabrizio

Abstracts
• Patrice Abry, SiSypH: Signals, Systems and Physics, a brief tour and Mutiscale anisotropic scale-free texture analysis for the Historic Photographic Paper Challenge
This talk will start by providing a brief overview of the research activities of the statistical signal/image processing team, SiSYPh, at the Physics Dept. at Ecole Normale Supérieure de Lyon.
Then, it will be shown how and why the developed anisotropic multiscale scale-free/multifractal texture analysis framework can be successfully applied to the classification of a large database of historic art photography papers, assembled by the MoMA (NYC).
Future challenges in multifractal texture analysis will also be envisaged.

Over the past thirty years, the ancient art of paper folding, or origami, has evolved into an interdisciplinary scientific field. Origami offers the possibility for new metamaterials whose overall mechanical properties can be programmed by acting locally on each crease. Origami metamaterials show for example auxetic behaviour (negative Poisson ratio) and multistability, the latter allowing reprogrammable configurations and deployable structures. Starting from a thin plate and knowing the properties of the material and the folding procedure, one would like to determine the shape taken by the structure at rest and its mechanical response. During this talk, we review some recent experimental and theoretical developments on the physics and mechanics of origami-based metamaterials.

• Nathalie Aubrun, A theoretical computer science approach to entropy
Subshifts of finite types (SFTs) are sets of colorings of $$\mathbf{Z}^d$$ which avoid some finite family of patterns. SFTs are thus defined by local interactions, and can thus model many real-world phenomena. These objects are of particular interest in statistical mechanics, ergodic theory and computability theory. In this talk we will focus on entropy of these systems, which measures the asymptotic growth of the number of allowed finite patterns. The entropy of one-dimensional SFTs can be easily computed from the graph representation of the subshift and its largest eigenvalue, and the possible values are algebraically characterized. In higher dimension, entropy of SFTs becomes uncomputable. We are nevertheless able to characterize the possible values, but very few examples of SFTs are known to have a close formula for entropy.
Slides

• Stefano Baroni, What I cannot compute, I do not understand: fathoming atomic heat transport from the struggle to simulate it
Modern simulation methods based on electronic-structure theory have long be deemed unfit to compute heat transport coefficients within the Green-Kubo formalism. This is so because the quantum-mechanical energy density from which the heat flux is derived is inherently ill defined, thus allegedly hampering the use of the Green-Kubo formulism. Every property that can be measured can also be computed, at least in principle: if it cannot, it's that the underlying theory is still incomplete. Steered by this conviction, we have derived an expression for the adiabatic energy flux from density-functional theory, which allows thermal transport to be simulated using ab initio equilibrium molecular dynamics. The resulting thermal conductivity is shown to be unaffected by the ill-determinacy of quantum mechanical energy densities and currents, by virtue of a hitherto unrecognized gauge invariance principle of thermal transport. In order to turn this new theory into a practical simulation tool, further insight is also needed into the statistical properties of finite time series, which I will also discuss if time allows. A few representative applications to thermal transport in elemental and molecular fluids will be presented.

• Marco Bertola, The role of Riemann—Hilbert  techniques in integrable systems, geometry,  spectral problems and stochastic point processes
A Riemann-Hilbert problem (RHP) is a particular type of boundary value problem for a matrix valued function on the complex plane (or other Riemann surface). It is the analytic tool, for example, to find holomorphic sections of vector bundles, the typical example being the Birkhoff factorization theorem on the Riemann Sphere. There is a surprisingly wide  plethora of problems that can be framed within the theory of RHPs; it includes the inverse spectral problem for integrable wave equations (KdV, mKdV, NLS, AKNS, and, to some extent, KP), the theory of occupation numbers for certain stochastic point fields, the theory of Painlevé equations and even the analysis of the spectral properties of certain inverse problems in tomography. Special techniques have been developed in the late '90 to study asymptotic behaviours of solutions of RHPs and this allows rigorous and very (extremely, in fact) detailed asymptotic analysis of nonlinear waves, be it in the long-time or small-dispersion regimes; for example results of "universality" of behaviour of solution near the caustic curve of the zero-dispersion approximation can be approached (if not outright solved) by such techniques. A "tau" function can be associated to the deformation space of any RHP; in special cases it becomes a Fredholm determinant, in others it takes the meaning of generating function of intersection numbers of characteristic classes on moduli spaces. In this talk I will try to give an overview of these topics to showcase the breadth and reach of the method, as well as my collaborators' research and my own.
Slides

• Giovanni Bussi, Using molecular simulations and NMR experiments to predict RNA structural dynamics
Ribonucleic acid (RNA) is acquiring a large importance in cell biology, as more functions that it accomplishes are discovered. However, experimental characterization of RNAs dynamical behavior at atomistic level is difficult. Molecular simulations at atomistic detail, in combination with state-of-the-art free-energy techniques and advanced analysis protocols, could in principle bridge the gap providing an unparalleled perspective on the mechanism and dynamics of RNA folding and conformational transitions. However, current empirical force fields used to model RNA are not yet accurate enough to predict structural dynamics in agreement with solution phase experiments. I will here show how the maximum entropy principle can be used to optimally combine molecular simulations and experimental data. A framework to model experimental errors will also be introduced. Applications of our approach to the determination of RNA structural dynamics will be presented, ranging from short oligonucleotide to larger biologically relevant non-coding RNAs.

• Pasquale Calabrese, Entanglement and thermodynamics in non-equilibrium isolated quantum systems
Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics. In the last decade the study of quantum quenches revealed that these two concepts are intricately intertwined. Although the unitary time evolution ensuing from a pure initial state maintains the system globally at zero entropy, at long time after the quench local properties are captured by an appropriate statistical ensemble with non zero thermodynamic entropy, which can be interpreted as the entanglement accumulated during the dynamics. Therefore, understanding the post-quench entanglement evolution unveils how thermodynamics emerges in isolated quantum systems. An exact computation of the entanglement dynamics has been provided only for non-interacting systems, and it was believed to be unfeasible for genuinely interacting models. In this talk I show that the standard quasiparticle picture of the entanglement evolution, complemented with integrability-based knowledge of the asymptotic state, leads to a complete analytical understanding of the entanglement dynamics in the space-time scaling limit.

• Sergio Ciliberto, Two new critical effects
We describe two new effects that appear close to the demixing critical point of two binary mixtures.
The first one is a surprising phenomenon consisting in a oscillating phase transition which appears
in a binary mixture (PMMA-Octanone) when this is enlightened by a strongly focused infrared laser beam. The dynamical properties of the oscillations are produced by a competition between various effects: the local accumulation of PMMA produced by the laser beam, thermophoresis, and nonlinear diffusion. We show that the main properties of this kind of oscillations can be reproduced in the Landau theory for a binary mixture in which a local driving mechanism, simulating the laser beam, is introduced.
The second effect that we describe is the observation of a temperature-controlled synchronization of two Brownian-particles in a binary mixture $$(C_{12}E_5-H_2O)$$ close to the critical point of the demixing transition. The two beads are trapped by two optical tweezers whose distance is periodically modulated. We notice that the motion synchronization of the two beads appears when the critical temperature is approached. In contrast, when the fluid is far from its critical temperature, the displacements of the two beads are uncorrelated. Small changes in temperature can radically change the global dynamics of the system. We show that the synchronisation is induced by the critical Casimir forces. Finally, we present the measure of the energy transfers inside the system produced by the critical interaction.

• Guido De Philippis, Spectral Optimisation problems with perimeter penalisation
Aim of the talk is to present some old and new results on existence and regularity for optimal shapes of spectral optimisation problems under perimeter constraint. A particular focus will be given to the case in which the considered perimeter is anisotropic, a case which (surprisingly) seems to present several additional difficulties. The talk is based on joint works with  B. Velichkov, M. Pierre,  J. Lamboley, M. Marini and J. Hirsch.

• Michele Fabrizio, A small taste of strong correlations
In the talk, I shall overview our activity on correlated electron systems by presenting two works that attempt to explain theoretically two intriguing results, one numerical and the other experimental.
The first is a puzzling outcome of numerical renormalization group applied to a two-channel Kondo model (2CK) with superconducting channels. Specifically, it was found that when the superconducting gap $$\Delta\to0$$, one does not recover the known spectrum of the 2CK at $$\Delta=0$$. We explain this result both qualitatively, by CFT arguments, and quantitatively, by extending the scaling approach by Anderson and Yuval to the case of gaped conduction baths.
The second work concerns a remarkable pump-probe experiment on $$K_3C_{60}$$, a molecular conductor that becomes superconducting below Tc= 20K. The sample is shot by an ultrashort laser pulse and the optical response is probed in time. When the laser frequency hits a mid-infrared absorption peak, a transient superconducting response is observed up to 200K, ten times higher than Tc. To explain this phenomenon, we first propose that the absorption peak is due to a spin-triplet molecular exciton. We next show that these excitons act as an entropy sink for quasiparticles, which thus cool down meanwhile the light pulse brings up the exciton population.
Slides

• Étienne Ghys, The three body problem
Three massive objects in space attract each other according to Newton’s gravitation law. Can one describe the dynamics of these objects in the long run ? This question is far too difficult, even Today. However, this problem has been a source of a huge quantity of new concepts in dynamical systems, symplectic geometry, topology, and ergodic theory, which are some of the main themes of research in the «geometry team» of UMPA. Starting from this example, I will try to describe some developments and, perhaps more importantly, some open questions.

• Alice Guionnet, Random tilings and Random matrices
I will survey how to study fluctuations in highly correlated systems such as random tilings and random matrices.
Slides

• Vincent Pilloni, Zeta functions
Given a system of polynomial equations with integral coefficients, one can try to compute the set of solutions over finite fields, the field of rational number and more generally number fields. The Zeta function of the system of equations  packages the information and makes it possible to formulate some deep conjectural correspondence with functional analysis and representation theory (Langlands).

• Andrea Romanino, Fundamental physics at SISSA
A brief introduction to the Physics Area of SISSA, focusing on the research in theoretical particle physics, astrophysics, and astroparticle physics.

• Gianluigi Rozza, Galerkin-RB-POD Reduced Order Methods: state of the art and perspectives with focus on parametric Computational Fluid Dynamics
In this talk, we provide the state of the art of Reduced Order Methods (ROM) for parametric Partial Differential Equations (PDEs), and we focus on some perspectives in their current trends and developments, with a special interest in parametric problems arising in Computational Fluid Dynamics (CFD). Systems modelled by PDEs are depending by several complex parameters in need of being reduced, even before the computational phase in a pre-processing step, in order to reduce parameter space. Efficient parametrizations (random inputs, geometry, physics) are very important to be able to properly address an offline-online decoupling of the computational procedures and to allow competitive computational performances. Current ROM developments in CFD include: a better use of stable high fidelity methods, considering also spectral element method, to enhance the quality of the reduced model too; more efficient sampling techniques to reduce the number of the basis functions, retained as snapshots, as well as the dimension of online systems; the improvements of the certification of accuracy based on residual based error bounds and of the stability factors, as well as the the guarantee of the stability of the approximation with proper space enrichments. For nonlinear systems, also the investigation on bifurcations of parametric solutions are crucial and they may be obtained thanks to a reduced eigenvalue analysis of the linearised operator. All the previous aspects are very important in CFD problems to be able to focus in real time on complex parametric industrial and biomedical flow problems, or even in a control flow setting, and to couple viscous flows -velocity, pressure, as well as thermal field - with a structural field or a porous medium, thus requiring also an efficient reduced parametric treatment of interfaces between different physics. Model flow problems will focus on few benchmark cases in a time-dependent framework, as well as on simple fluid-structure interaction problems. Further examples of applications will be delivered concerning shape optimisation applied to industrial problems.
Slides

• Henning Samtleben, String compactifications and exceptional geometry
Generalised and exceptional geometry have emerged over recent years as powerful tools for the description and the analysis of string compactifications. In particular, they yield manifestly duality covariant formulations of supergravity theories. I review recent constructions and applications.
Slides

• Denis Serre, Hilbert metric, singular elliptic PDEs and gas dynamics
We consider a boundary-value problem for a rather singular elliptic PDE. The data is a bounded convex planar domain. This BVP occurs in several situations, among which the Riemann problem for a Chaplygin gas, or the parametric case of complete minimal surfaces in negative ambiant curvature. Because the PDE fails to be uniformly elliptic, it is classical that we need to establish an a priori estimate in Lipschitz norm. This task turns out to be quite simple when using the Hilbert metric.
Slides

• Sandro Sorella

• Cédric Vaillant, Epigenomics in 3D: modeling the dynamic coupling between epigenome and chromatin organization
Cellular differentiation occurs during the development of multicellular organisms and leads to the formation of many different tissues where gene expression is modulated without modification of the genetic information. These modulations are in part encoded by chromatin-associated proteins or biochemical tags that are set down at the chromatin level directly on DNA or on histone tails. These markers are directly or indirectly involved in the local organization and structure of the chromatin fiber, and therefore may modulate the accessibility of DNA to transcription factors or enzymatic complexes, playing a fundamental role in the transcriptional regulation of gene expression. Statistical analysis of the repartition of this epigenomic information along the chromosomes have shown that genomes of higher eukaryotes are linearly partitioned into domains of functionally distinct chromatin states. In particular, experimental evidence has shown that the pattern of chromatin markers along chromosomes is strongly correlated with the 3D chromatin organization inside the nucleus. This suggests a coupling between epigenomic information and large-scale chromatin structure. Recently, using polymer physics and numerical simulations, we showed that attractive interactions between loci of the same chromatin state might be the driving forces of the folding of chromatin inside the nucleus [1]. In this study, we assumed that the epigenomic information pre-exists to the 3D organization. However, increasing number of experimental results suggests that chromatin marks are themselves highly dynamic during cell cycle or developmental stages and that 3D organization of chromatin might play a key role in the stabilization and function of chromatin markers. We will describe our efforts to better understand the crosstalk between the epigenome and the 3D organization by introducing an original theoretical framework, the so-called "Living Chromatin model" (LC model) where the dynamics of chromatin markers deposition along chromosomes will be coupled to the 3D folding of the chromatin fiber. As a main outcome, we show how the spatial folding of chromatin can indeed strongly influence the establishment and the maintenance of extended epigenomic domains. We discuss the implications of these results in various biological systems like the formation and dynamics of topologically-associated domains in drosophila or the establishment of dosage compensation in worm and mammals.
Slides