Symmetry and Computation
Symétries dans les méthodes de calcul
Tuesday 3 (9 am) – Saturday 7 (12 am) April 2018
Comité scientifique & Comité d’organisation
Evelyne Hubert (INRIA – Sophia Antipolis)
Elizabeth Mansfield (University of Kent)
Hans Z. Munthe-Kaas (University of Bergen)
Agnes Szanto (North Carolina State University)
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Symmetry appears as a desirable feature to preserve through numerical computations, as a property to take advantage of in efficiency consideration, or as an organizing principle for computations. In either cases, sophisticated schemes that require group-theoretic foundations have been developed, as the results of research at the frontier of pure mathematics, computer science and applied mathematics. This meeting aims at creating new interactions between several different trends of group theoretic approaches in computation. The goal is to bring out the fundamental issues and uncover foundational concepts and results underlying the different methods that shall provide the guiding principles in further developments.
The topics will range across Geometric Integration, Symbolic Analysis, Computational Algebraic Geometry, Orthogonal Polynomials and Special Functions but with a focus on the exploitation of symmetry and group theoretic methods. |
La symétrie est une propriété à préserver dans les calculs numériques, à exploiter pour améliorer l’efficacité des calculs algébriques, où sous-tendent les meilleures pratiques. Des méthodes sophistiquées à base de considérations sur les groupes ont été développées à l’interface des mathématiques pures, de l’informatique et des mathématiques appliquées. En nous concentrant sur l’exploitation ou la préservation des symétries, nous aborderons des sujets portant sur l’intégration des systèmes différentiels, la résolution des systèmes polynomiaux et l’utilisation des polynômes orthogonaux multivariés en calcul numérique et algébrique.
Cette rencontre a pour but de favoriser les interactions entre les différentes branches des mathématiques computationnelles qui traitent avec les symétries et la théorie des groupes. Nous espérons voir émerger des problèmes et concepts fondamentaux communs aux différentes approches et ainsi permettre d’énoncer des principes généraux pour de futurs développements. |
Gianluca Frasca-Caccia (University of Kent) Simple bespoke finite difference methods that preserve conservation laws
Pascal Chossat (Université de Nice Sophia-Antipolis) Computational aspects of equivariant bifurcation theory
Peter Clarkson (University of Kent) Orthogonal Polynomials and Integrable Systems
Guillaume Dhont (Université du Littoral Côte d’Opale) Symbolic interpretation of the generating function in invariant theory
Emilie Dufresne (University of Nottingham) Toric reparametrization of linear compartment models
Kurusch Ebrahimi-Fard (Norwegian University of Science and Technology) Magnus expansion and Lie group integrators
Willy Hereman (Colorado School of Mines) Continuous and Discrete Homotopy Operators with Applications
Evelyne Hubert (INRIA – Sophia Antipolis) Invariants of ternary forms under the orthogonal group – VIDEO –
Alexander Hulpke (Colorado State University) A survey of group theoretic algorithms
Peter Hydon (University of Kent) Geometric structures for difference equations
Arieh Iserles (University of Cambridge) Skew-symmetry and computation
Boris Kolev (Aix-Marseille Université) Invariants and covariants in Solid Mechanics
Niclas Kruff (RWTH Aachen University) Coordinate-independent criteria for Hopf bifurcations
Gloria Mari Beffa (University of Wisconsin) Evolutions of polygons and soliton equations
Dominique Manchon (CNRS Université Clermont-Auvergne) The Hopf algebra of Lie group integrators and planarly branched rough paths
Elizabeth Mansfield (University of Kent) Noether’s Theorem, then and now
Hans Z. Munthe-Kaas (University of Bergen) Symmetry and computation: a few of my favourite things – VIDEO –
Marc Olive (ENS Cachan) About Gordan’s algorithm for binary forms
Peter Olver (University of Minnesota) Computation with moving frame
Sheehan Olver (Imperial College) Representation theory of the symmetric group, numerically
Linyu Peng (Waseda University) Symmetries of Differential-Difference Equations and Noether’s Conservation Laws
Fabian Reimers (Technical University Munich) Separating Invarians of Finite Groups
Cordian Riener (Aalto University) Computing the homology of symmetric semi-algebraic sets
Ana Rojo-Echeburúa (University of Kent) Discrete moving frames, evolution of curvature invariants and discrete integrability
Alexander Schmeding (TU Berlin) Shape analysis on homogeneous spaces
Cheri Shakiban (University of St. Thomas) Applications of cumulative distance histograms in diagnosing breast cancer
Maurits Silvis (University of Groningen) Symmetry constraints for the modeling and numerical simulation of turbulent flows
Michael Singer (North Carolina State University) Walks, Groups, and difference equations
Ari Stern (Washington University in St. Louis) Hybrid finite element methods preserving symmetries and conservation laws – VIDEO –
Agnes Szanto (North Carolina State University) Subresultants, Multivariate Symmetric Interpolation, Jacobi Polynomials
Olivier Verdier (Bergen University College) Symmetries in Numerical Analysis
Sebastian Walcher (RWTH Aachen) Dimension reduction for chemical reaction equations
Jacques-Arthur Weil (Université de Limoges) Symmetries of linear differential systems and their relation to Galois groups
Yuan Xu (University of Oregon) Symmetry and cubature rules
Michele Zadra (University of Kent) Moving frames and conservation laws: a linear action of SU(2)
Posters
Noureddine Benhamidouche (Université de M’sila) General self similar solutions and contour enhancement via nonlinear degenerate parabolic
equation
Florent Bréhard (ENS Lyon) A Newton-like Validation Method for Chebyshev Approximate Solutions of Linear Ordinary Differential Equations
Michela Ceria (Università degli Studi di Trento) Combinatorics of involutive divisions
María Jesús de la Puente (Universidad Complutense, Madrid) Volume of alcoved polyhedra and Mahler conjecture
Evelyne Hubert (INRIA – Sophia Antipolis) Computing Symmetric cubatures: A moment matrix approach
Nelson Martins Ferreira (Polytechnic Institute of Leiria) On the structure of a triangulation
Maurits Silvis (University of Groningen) Symmetries and conservation laws as constraints for the modeling and numerical simulation of turbulent flows