See the Google Agenda of the colloquium, and add the iCal url to your calendar
Next session
Thursday, May 7th, 2026, 10h30 Salle de séminaire du CERMICS
Dynamical low-rank approximation and time integration of tree tensor networks
The talk first presents some numerical experiments with time-dependent tree tensor network algorithms for the approximation of quantum spin system dynamics. It continues with the basics in the design of time integration methods that are robust to the typical presence of small singular values, that have good structure-preserving properties (norm, energy conservation or dissipation), and that allow for rank (= bond dimension) adaptivity and for parallelism. The discussion of basic concepts forms the main part of the talk and will be done for the smallest possible type of tensor network differential equations, namely low-rank matrix differential equations, which are of interest in their own right. Once this technically simplest, yet nontrivial case is understood, there is a systematic path to the extension of the low-rank integrators and their favourable properties to general tree tensor networks.
This talk is based on joint work with many colleagues and former and present students, among which I wish to single out Othmar Koch for the first mathematical work on dynamical low-rank approximation (DLRA) in 2007, Ivan Oseledets for jointly discovering the first robust DLRA integrator in 2014 (the projector-splitting integrator), Gianluca Ceruti and Jonas Kusch for jointly developing the Basis Update & Galerkin (BUG) integrators since 2022, and Hanna Walach, Gianluca Ceruti, Dominik Sulz and Charlotte Verhoeven for the recent systematic extension from low-rank matrices to general tree tensor networks both in theory and in increasingly efficient implementations.
Past sessions
January 15 2026, 15h30: Bertrand Maury,
Académie des Sciences et Université Paris-Saclay,
Dégénérescences hilbertiennes.
October 17 2025, 16h: Timothy Gowers,
Collège de France and University of Cambridge,
Applications of Shannon entropy in combinatorics.
April 10 2025, 14h: Josselin Garnier,
Académie des Sciences et École polytechnique,
Utilisation de modèles d’ordre réduit pour l’imagerie par ondes. (slides),
November 20 2024, 14h: François Golse,
École polytechnique,
Distance de Wasserstein et observabilité en dynamique quantique. (slides),
May 22 2024, 10h: Nalini Anantharaman,
Académie des Science et Collège de France,
Trou spectral des surfaces hyperboliques aléatoires.
February 9 2024, 10h30: Andrea Lodi,
Cornell Tech,
Mixed-Integer Programming: 75 years of history and the Artificial Intelligence challenge. (slides),
December 14 2023, 15h: Andrew Stuart,
Caltech,
Learning Solution Operators For PDEs: Algorithms, Analysis and Applications. (slides),
June 8 2023, 14h: Peter K. Friz,
TU and WIAS Berlin,
Reconciling Itô and rough path theory. (slides),
April 19 2023, 14h: Maciej Zworski,
University of California, Berkeley,
Magic angles in the chiral model of twisted bilayer graphene. (slides),
December 12 2022, 14h: Jean-Bernard Lasserre,
CNRS, Université de Toulouse,
Moments, positive polynomials and the Christoffel function. (slides),
March 10 2022, 14h: Hugo Duminil-Copin,
IHES, Université de Genève,
Symétries émergentes en physique statistique planaire. (slides),
October 6 2021, 14h: Benoît Perthame,
Académie des Sciences, Sorbonne Université,
Structured equations in biology. (slides),
January 22 2020, 14h: Jean-Michel Coron,
Académie des Sciences, Sorbonne Université,
Comment utiliser les non-linéarités pour contrôler un système. (slides),
January 22 2020, 10h: Serge Abiteboul,
Académie des Sciences, ENS/Inria, ARCEP,
Responsible data management. (slides),
November 12 2019, 14h: János Pach,
Renyi Institute Budapest and MIPT Moscow, Bézout Chair 2019,
How to escape the curse of dimensionality in combinatorics.
September 20 2019, 10h: Stéphane Mallat,
Collège de France et Académie des Sciences,
Mathematical Mysteries of Deep Neural Networks. (slides),
June 25 2019, 10h: Alice Guionnet,
ENS Lyon et Académie des Sciences,
Entropie et grandes déviations en théorie des matrices aléatoires.
January 10 2019, 10h: Frank Merle,
Université de Cergy-Pontoise et IHES,
Asymptotics for Critical Nonlinear Dispersive Equations. (slides),
November 20 2018, 10h: Felix Otto,
MPI Leipzig,
Randomness in Partial Differential Equations. (slides),
October 25 2018, 9h: R. Tyrrell Rockafellar,
University of Washington,
Part I: The Role of Convex Analysis in Optimization. (slides),
Part II: Progressive Decoupling of Linkages in Optimization with Elicitable Convexity. (slides),
September 4 2018, 14h: Carsten Carstensen,
Humboldt-Universität zu Berlin, Germany,
Discontinuous Petrov-Galerkin Schemes. (slides),
June 7 2018, 15h30: Bjorn Engquist,
The University of Texas at Austin,
Multiscale dynamical systems and parareal algorithms. (slides),
May 31 2018, 15h15: Arturo Kohatsu-Higa,
Ritsumeikan University,
IPB pour diffusions arrêtées.
May 18 2018, 16h: Panagiotis Souganidis,
The University of Chicago,
Nonlinear stochastic partial differential equations. (slides),
March 5 2018, 10h30: Yann Brenier,
ENS,
Le problème de Cauchy pour les systèmes de lois de conservation entropiques traité par minimisation convexe. (slides),
December 18 2017, 14h: Laure Saint-Raymond,
ENS de Lyon et Académie des Sciences,
Forçage quasi-résonnant d’ondes internes dans un domaine avec topographie (en collaboration avec Yves Colin de Verdière).
October 4 2017, 15h30: Daniel Kuhn,
EPFL,
Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations.
June 15 2017, 10h: Arnak Dalalyan,
ENSAE,
On the Exponentially Weighted Aggregate with the Laplace Prior.
October 17 2016, 14h: Mitchell Luskin,
University of Minnesota,
Mathematical Modelling of Incommensurate Materials.
June 7 2016, 10h: Common seminar CERMICS/IMAGINE,
-
10h: Mathieu Aubry,
IMAGINE, École des Ponts ParisTech
Representing 3D models for matching and retrieving. (abstract) -
11h: Francis Bach,
Inria et ENS
Beyond stochastic gradient descent for large-scale machine learning. (slides), (abstract)
March 30 2016, 14h: Emilie Kaufmann,
CNRS,
Multi-armed bandit models: a tutorial. (slides),
November 30 2015, 14h: Hugo Touchette,
National Institute for Theoretical Physics,
Théorie des grandes déviations : des mathématiques à la physique. (slides),