Institut de recherche mathématique avancée

Résumé : A : The Horn Problem
P-A : Invariant distances on Legendrian spaces
A : How to count the discriminant points of a contact isotopy?
A : Existence of Hamiltonian chords in symplectic geometry

Résumé : M : TBA N : Geometry of third order differential equations
C : Flow categories as exit path categories
F : Circle Homeomorphisms and 3-Dimensional Geometry

Résumé : Abstract : The lifted TASEP is a variant of the totally asymmetric exclusion process where at each time-step, instead of trying to move forward a uniformly chosen particle, we try to move forward a marked particle which then may pass the marker to another particle. It was introduced by physicists as a toy model for non-reversible event-chain Monte-Carlo algorithms, which are expected to reach equilibrium faster than reversible dynamics. We will study the behaviour of this system on the integer line by evidencing a connexion with true self-avoiding walks, yielding timescales of the dynamics. This is based on joint work with Clément Erignoux, Werner Krauth, François Simenhaus and Cristina Toninelli.

Résumé : In recent years, conservative-characteristic methods have been extensively used to numerically solve different hyperbolic PDEs. These methods use a combinaton of a finite volume method to approximate the cell-averages in mesh cells using conservative form of equations, and an arbitrary method to approximate the point values in edges/faces of the mesh using the non-conservative form of equations. Therefore, the overall method remains conservative (for the averages), retaining a lot of flexibility in how to deal with the point values. In this talk, we will describe 2 of such methods: CABARET and Active Flux, including some applications for both schemes.

CABARET, first introduced by V. Goloviznin and later refined by S. Karabasov [1], is a second-order explicit conservative-characteristic method. Its special feature is the extrapolation of Riemann invariants along the linearized characteristics to evolve the point values. We will discuss this method in detail and introduce various applications for problems in oceanology [2], fluid-structure interaction [3], transonic flows [4] and thermoacoustic instability [5].

Active Flux method, first introduced by T. Eymann and P. Roe [6], has been adapted to solve many problems for hyperbolic systems of PDEs on orthogonal and polygonal meshes. There are many versions of this method, and we will concentrate on the work of R. Abgrall and his group. This version of Active Flux is a third-order scheme [7], which works on general polygonal meshes (for 2D) and uses the method of lines to approximate the point values on edges and nodes of the mesh. We will describe the base algorithm for two-dimensional problems on a plane, and also we introduce the generalization of Active Flux method on triangular meshes to hyperbolic problems on a sphere [8].

References:

[1] S. Karabasov and V. Goloviznin “Compact Accurately Boundary-Adjusting High-REsolution Technique for Fluid Dynamics”, Journal of Computational Physics, 228(19), pp. 7426–7451, 2009.

[2] V.M. Goloviznin, P.A. Maiorov, P.A. Maiorov and A.V. Solovjev “Validation of the Low Dissipation Computational Algorithm CABARET-MFSH for Multilayer Hydrostatic Flows with a Free Surface on the Lock-release Experiments”, Journal of Computational Physics, 463, p. 111239, 2023.

[3] N. Afanasiev, V. Goloviznin, P. Maiorov and A. Solovjev “Simulating the dynamics of a fluid with a free surface in a gravitational field by a CABARET method”, Mathematical notes of NEFU, 29(4), pp. 77–94, 2022.

[4] N. Afanasiev and V. Goloviznin, “A Locally Implicit Time-Reversible Sonic Point Processing Algorithm for One-Dimensional Shallow-Water Equations”, Journal of Computational Physics, 434, p. 110220, 2021.

[5] N. A. Afanasiev, V. M. Goloviznin, V. N. Semenov et al. “Direct simulation of thermoacoustic instability in gas generators using the cabaret scheme”, Mathematical Models and Computer Simulations, 13(5), pp. 820–830, 2021.

[6] T.A. Eymann and P.L. Roe. “Active flux schemes”, AIAA, 382(19), 2011.

[7] R. Abgrall, J. Lin and Y. Liu “Active flux for triangular meshes for compressible flows problems”, Beijing Journal of Pure & Applied Mathematics, 2(1), pp. 1–33, 2025.

[8] N. Afanasev and R.Abgrall “Active Flux Method on a Sphere”, Submitted, 2025.

Résumé : On one hand, compilers successfully automate many important optimizations. On the other hand, compilers often miss critical optimizations, especially when they are general-purpose. A striking example of this is how compilers typically fail to reason about approximating exact arithmetic with finite precision number representations. Due to such compiler limitations, high-performance code is still commonly optimized by hand and packaged into optimized libraries, which is time-consuming and error-prone.

In the first part of this talk, I will present, at a high level, my ongoing work aimed at replacing manual optimization with an interactive optimization process that combines human expertise with compiler automation. In the second part of this talk, I will dive deeper into one strand of this work, which is aimed at combining program optimization with guaranteed numerical accuracy.

About the speaker : Since one year, I am a CNRS researcher in the CAMUS / ICPS team of ICube, in Strasbourg, France. Before joining CNRS, I was a postdoctoral researcher in the same team for almost two years. I received my PhD from the School of Computing Science at the University of Glasgow, in Scotland, supervised by Michel Steuwer and Phil Trinder. I received my Master from Sorbonne Université in Paris, France.

https://thok.eu/
https://www.ins2i.cnrs.fr/fr/cnrsinfo/thomas-koehler-et-loptimisation-de-programmes